As the Yankees’ braintrust huddled at the team’s Tampa headquarters, where GM Brian Cashman & Co. planned to ride out this week through Thursday’s 6 p.m. trade deadline, they learned some very crucial intel from the Mets.

The price tag on top-shelf relievers over these final 24 hours is soaring, and likely going up from here, thanks to the arms race that rapidly developed Wednesday in the NL East over the span of a few minutes.

Mets’ president of baseball ops David Stearns telegraphed his intentions at the start of this month, publicly declaring his priority to be as much relief help as he could get his hands on. Once again, he made good on that pledge Wednesday with a pair of bullpen-fortifying trades involving Giants submariner Tyler Rogers and Cardinals flamethrower Ryan Helsley.

Stearns sacrificed his No. 10 prospect (Blade Tidwell) and No. 12 (Drew Gilbert) along with serviceable-reliever Jose Butto to land Rogers. About an hour later, the Mets shipped No. 8 Jesus Baez, No. 14 Nate Dohm and minor-leaguer Frank Ellisalt to St. Louis for Helsley.

Good thing, too. Because in-between, the Phillies netted the biggest prize of the bullpen market in Jhoan Duran, and paid the exorbitant price of a No. 4 (catcher Eduardo Tait) and a No. 6 (pitcher Mick Abel).

Both Rogers and Helsley are rentals, unlike Duran, who now shapes up to be a problem for the Mets well into the future, as he’s under team control through 2027 (hence the sticker bump). Every contender is on the prowl for at least one bullpen arm, with most trying for multiple, which Stearns already has accomplished by loading up on Rogers, Helsley and Gregory Soto in the span of six days.

The prospect cost for Rogers, however, was steep in that Tidwell and Gilbert are close to being productive MLB pieces. The high-ceiling Baez, a 20-year-old infielder, is at low-A St. Lucie while Dohm, 22, is pitching for high-A Brooklyn (2.62 ERA, 11.3 K/9).

Tidwell, who turned 24 last month, is a hard-thrower (regularly touching 99 mph) who still looked raw in four appearances (two starts) for the Mets this season, but that fastball should land him an MLB job before too long. Gilbert, you may remember, was part of the Mets’ return for Justin Verlander — first baseman Ryan Clifford was the other piece — and the centerfielder got hot at Triple-A Syracuse just in time for Stearns, hitting .316 with six homers and a 1.033 OPS over his last 20 games.

Those were two valuable chips. But for Stearns, it was all about doing what needed to be done, and the Mets’ farm system — long a hinderence for deal-making — is now at the stage where there’s plenty of trade capital. Plus, Helsley and Rogers are as close as to sure things as you can get this time of year. Helsley, a battle-tested closer, throws 99 mph (41 Ks/36 IP) and Rogers (1.80 ERA, 0.86 WHIP, 53 appearances) has a 2.1% walk rate that suggests he’s won’t be driving manager Carlos Mendoza nuts in the late innings.

As for the Yankees, they’ve also been shopping over the past week, but Stearns apparently jumped them in the relief market and Cashman badly needs some bullpen help. Trading for Ryan McMahon last Friday was critical in the sense that the Yankees didn’t have a capable third baseman on the roster. And so far, McMahon has done everything Cashman had envisioned — stellar defense, with decent production at the plate (even if another two years and $32 million seems like an overspend).

After McMahon, Cashman went to work improving the Yankees on the margins, first by bringing in the super-utility man Amed Rosario, the former Met, and then Wednesday’s trade for Austin Slater, another righty-slugging weapon to use against lefty pitchers. While both are upgrades to a roster that thinned out real fast, these two aren’t exactly paving a path to the World Series for the Yankees, as much as it now hands manager Aaron Boone some additional possibilities at third base and leftfield.

“We haven’t had that luxury here a lot of years,” Boone said. “So having more of that moving-parts flexibility gives you some opportunities at key moments of the game to create a platoon advantage.”

That’s fine. With McMahon, Rosario and Slater, the Yankees are a better team than they were a week ago. But Cashman surely knows he has more significant work to before Thursday’s deadline, as another shutdown reliever is a must and maybe even a starter, considering that the Yankees’ rotation is stacked with question marks after Max Fried and Carlos Rodon.

A few months back, this figured to be a re-tooling period for a return trip to the World Series. Instead, the Yankees are fighting for survival, mired in a wild-card race that has four teams separated by 1 1/2 games.

“I know the boys are in Tampa grinding away at it, having a million conversations and a lot of balls in the air,” Boone said. “So we’ll see. There’s no guarantees. I would love for us to be able to add a piece or two — on the mound or in some way, shape or form to make us a better club.”

The Mets and Phillies were busy doing that Wednesday. Now that we’re closing fast on the deadline’s final hours, it’s getting late for the Yankees to show just how serious they are about October.