When word surfaced Tuesday night that the Mets were circling on Carlos Correa, I reached out to team officials who diminished the possibility of such a union.

And, indeed, a few hours later, Correa was in agreement with the Giants on a 13-year, $350 million megadeal.

But the eleventh-hour belief that the Mets were lurking accentuated who the Mets are these days. This is what it was like in George Steinbrenner’s heyday. Yankees officials would state they were not interested in a star. Yet a not-insignificant segment of the game wouldn’t accept that. They needed to see a signed contract or a press conference with another team before they truly believed.

There was a bogeyman element to Steinbrenner’s Yankees. They were out there stalking. Anything felt possible.

Like the Steve Cohen Mets.

Up until the wee-hours newsbreak that Aaron Judge was re-signing with the Yankees, there was a highly ranked executive from another team predicting that Cohen would enter late, trump all offers and steal the Yankees’ best player because, well, he could. It is what he tried to do with Correa.

The luxury tax was implemented two decades ago with Steinbrenner in mind, as a way to penalize spending at the upper levels to attempt to slow him down. The collective bargaining agreement reached last offseason introduced a fourth tax threshold with the most sizable penalties ever. It was designed with one person in mind and quickly became known as The Steve Cohen Tax.

Cohen, though, has treated that “deterrent” as if he were being told fries cost extra with his dinner. Cohen’s initial intention this offseason was to keep his payroll in the same $300 million range as it was last year. But as it became clear prices were going to spike this offseason — as they always do a year after a new CBA is finalized and labor peace can be counted upon for a while — he asked himself a pertinent question: Why? The money was not an issue when it came to going beyond $300 million. And his hunger was to win. Now.

So the Mets project a payroll of approximately $350 million, which, with luxury-tax penalties of more than $70 million, currently means Cohen will be spending roughly $420 million on major league players in 2022. It is possible there is pruning to come — notably the $14 million 2023 salary of Carlos Carrasco is in play.

But the Mets also are not done adding. Maybe the big stuff is done — at least until the trade deadline. Yet who knows with the Cohen Mets? The paranoia within the game now is that the Mets are in on everything big until proven otherwise. Cohen is the great white shark in Jaws. Out there. Waiting to strike.

In the old Mets days BC — Before Cohen — when a Mets official would use a term such as “being opportunistic” to describe the current acquisition posture of the team, you would brace yourself for the 30th re-signing of Rene Rivera.

On Tuesday morning, a Mets official used the term “being opportunistic” about where the team stood after exceeding a $300 million payroll. By the evening, Cohen opportunistically was trying to see whether there was a late avenue to navigate to land Correa to play next to Lindor. To do essentially what Steinbrenner once approved by putting Alex Rodriguez next to Derek Jeter.

Correa, though, was far down the line with the Giants and did not need a last-second save from Cohen’s wallet.

A Mets official suggested the Mets now are on the finer details of roster construction. But, as with Steinbrenner in the old days, let’s wait for the press conference elsewhere before ruling the Cohen Mets out of anything. Still, let’s use 3Up to delve into what finishing off the most expensive roster in history might look like:

1. By signing Justin Verlander and Jose Quintana to two-year contracts and Kodai Senga for five years, the Mets know they will have three starters (health/performance permitting) for the 2024 season. Max Scherzer can opt out after this season, and because Scherzer himself was at the vanguard of showing short-term, big-money deals are available for elite older starters, it would be a shock if he did not opt out (health permitting), unless Cohen comes in with a preemptive extension.

But in 2023, the Mets also should learn more about whether Tylor Megill and David Peterson can be trusted to be full-time starters moving forward.

Plus, I am willing today to put the Mets into next offseason’s Shohei Ohtani sweepstakes unless he announces on Day 1 he does not want to play in Queens.

Overall, the Mets might not be in as desperate a spot for rotation help next offseason as they faced this offseason, especially if Senga proves he is a top-of-the-rotation starter in MLB and/or Megill and Peterson graduate to no-question starters.

Still, if they could make it happen, the Mets want more controllable starting pitching with upside, in part because their farm system might not be ready to deliver rotation arms even after this season. If the Mets move Carrasco, that is what they are looking for in return. They might have to include a prospect with Carrasco to get it done.

But they are probably better positioned to use prospects now. They had four picks in the first two rounds of last year’s draft, and GM Billy Eppler mentioned at the time that the Mets did not trade any of their 19 best prospects (by internal rankings) during last year’s trade deadline (I’m not sure that is a good thing). Plus, by giving the qualifying offer to Chris Bassitt and Jacob deGrom and having them sign elsewhere, the Mets will pick up two compensation draft picks after the fourth round this coming June.

The Mets want to protect as much of the quality and quantity of their system as possible. Remember that Cohen said he wanted to follow the Dodgers blueprint under their current ownership, which was to use free-agent money early to protect the farm system until it was deep enough to regularly provide both talent for the major league team and trade fodder.

One of the tensions for the Mets throughout this year will be the counterbalance of protecting the system for the big picture and being arguably the most win-now team in the sport.

2. At this moment, the bullpen needs to be addressed more than the rotation. With the retention of Edwin Diaz and the additions of David Robertson and Brooks Raley, the Mets at least have a unit to attack the final nine outs. Raley gives them the kind of legit lefty they lacked in the pen last year. Since returning from the Korean Baseball Organization after the 2019 season, Raley has allowed a .166 batting average to lefty hitters.

If the Mets trade Carrasco, I believe the plan is to start Peterson to, among other reasons, have two lefty starters (with Quintana) in the rotation. The Mets would have a tough decision on whether to keep Megill’s power arm in the bullpen or to stretch him out at Triple-A to stay ready to start when the inevitable injuries strike.

Either way, the Mets probably still need two relievers to join Drew Smith as both reliable depth and to give Buck Showalter even more options for the final nine outs.

This offseason began with a strong belief that the Mets would re-sign Adam Ottavino. And that is still possible. But clearly there is a discrepancy in how the two sides see the righty’s value. If not Ottavino, Mychal Givens is still available, as is David Phelps. There were teams interested in Seth Lugo as a starter, and if he follows that route, a reunion with the Mets is unlikely. The home run would be to figure out how to pair Alexis Diaz with his older brother, Edwin. But the Reds would need some of the better Mets prospects in a trade to get that done.

As far as a second lefty, the Mets can decide they are fine with Raley and the righties Diaz and Robertson, who both excel at getting lefty hitters out. But why would Cohen skimp on trying to have it all? Matt Moore’s first full season as a reliever went terrifically for the Rangers. He still walked too many, but countered by striking out 27.3 percent of opposing hitters while dominating righties (.165 batting average) and not giving up a homer to any of the 84 lefties he faced. But was that an aberration? Will the Mets regret trading Thomas Szapucki as part of the package for Darin Ruf? It was just 13 ⅔ major league relief innings for the Giants, but Szapucki struck out 29.6 percent of batters. Is there any doubt the Mets would be better off with J.D. Davis and Szapucki than with Ruf?

The other intriguing free-agent lefty is Zack Britton. His three Yankees appearances last season after returning from Tommy John surgery were terrible (he walked six of the nine hitters he faced). A team would have to convince itself he rushed back too soon and would be effective further removed from the surgery. If the Mets believe that, is this a place Cohen’s money could be effective? Maybe some team is willing, off of history and reputation, to give Britton a strong guarantee. But, if not, what if the Mets gave Britton a low base such as $1 million-$2 million along with a chance to get to, say, the $14 million he earned last year in appearances bonuses along the way.

This is my totally-made-up example: Britton gets $2 million in 2023 as a base salary, then a $1 million performance bonus for each of 15, 20, 25 and 30 games and a $2 million bonus for each of 35, 45, 55 and 65 games. The Mets would only be using him frequently if he were healthy and effective.

3. The Mets’ DH/backup outfield situation is right now Ruf, Daniel Vogelbach and Khalil Lee — with the option of using Jeff McNeil in the corner outfield if needed. That is like having a tarp on a mansion. It is a reminder that not even $350 million buys everything. There is no such thing as a defect-free roster.

The agreement with lefty-swinging catcher Omar Narvaez opens a path for a variety of moves, including trading at least one catcher.

But everything is complicated by what the Mets cannot know right now — do Francisco Alvarez and/or Brett Baty and possibly Mark Vientos help solve offensive issues that keep the team from needing to be too bold in adding a bat. The Mets also remain open to the possibility that switch-hitting Ronny Mauricio, who has performed well in the Dominican Winter League mixing in some third base besides shortstop, could be a factor before the end of the 2023 campaign.

Still, with so much invested in 2023, the Mets have to add at least one more bat for comfort. It would be great if that bat could play center field and hit lefty pitching. That is a difficult needle to thread.

Free agent Adam Duvall won a Gold Glove in 2021 moving around the outfield while serving as the primary center fielder during the playoffs for the champion Braves. However, Duvall missed the second half last year after tearing the tendon sheath in his left wrist. I have seen Aaron Hicks and Mark Teixeira return from that injury, and it is a particularly problematic one for a hitter. Plus, Duvall, despite being righty, has not been a lefty masher throughout his career.

The Mets had middle-of-the-pack results against southpaws last year, in part because Davis and then Ruf never provided that weapon versus lefties the Mets envisioned. Would Ruf do it in Year 2 with the organization, or is he cowed by New York? Will Alvarez provide it as both a catcher and DH?

Brandon Drury cannot play center field, but he can be used at several positions and DH. But you would have to believe his 2022 breakout (28 homers, .813 OPS) is real because he probably is in line for a multi-year contract. Free agent A.J. Pollock has a history of hitting lefties well, but probably is not trustworthy in center any longer.

Even in a down 2022, J.D. Martinez still had a .998 OPS against lefties. However, Martinez, 35, is now strictly a DH (the Red Sox did not use him in the field once last year). Do the Mets want to have a full-time DH? Probably not, because Showalter wants to find ways to keep the bats of, for example, Lindor and Pete Alonso in the game even when they don’t play the field. The Mets can live with just adding a bat and having Mark Canha and Starling Marte as the backups to Brandon Nimmo in center. They would then have to make sure to stash a Four-A-type center fielder at Triple-A. Maybe Travis Jankowski will become Cohen’s Rene Rivera.

Almost the ideal fit would be Sam Haggerty. It is easy to forget the Mets once obtained him for Walker Lockett, but then lost him on waivers in January 2020 to the Mariners. Last year, he blossomed into an outstanding fourth outfielder capable of playing any of the three positions plus producing an 1.100 OPS against lefties as a switch-hitter. Is that sustainable? It is fascinating that Seattle has become a place where failed Mets (Chris Flexen, Paul Sewald) grow into something much better.

Could the Astros’ Chas McCormick or the Rays’ Manny Margot be available in a trade?

The Mets do not have to be wedded to a righty hitter or center field option. Both Ruf and Vogelbach can move to strictly bench roles or perhaps — with not substantial contracts for 2023 — could be traded. Maybe there is still a big bat to come. Do the Mets still see Michael Conforto as a big bat? Could there be a reunion?

As we have learned with Cohen, keep an open mind.