My take is that overall the bullpen did a good job yesterday and that Cora's decisions were borderline prescient.
Your chief complaint seems to be Cora waiting too long to pull Pivetta.
But Illinoisox has pointed out that things happened too quickly in the 6th inning to have any chance of warming up a reliever in time. Specifically, the first two baserunners--an HBP followed by a single--were on base after just 3 pitches, which was much too soon to get someone on the mound for the 3d batter.
And the third batter, LeMahieu, was the guy who made the biggest difference with the double that brought in 1 run and put runners on 2d and 3d with no one out. Then Judge flied out with no one one scoring. However, Torres then hit a ground ball single to right to bring home the Yankees 2d and 3d runs. Pivetta walked Stanton before Llovera came in to get the final two outs with no more Yankees runs scored.
And the Yankees won 3-2 because the Sox couldn't score a run after their 2 runs in the 4th. It's perhaps worth noting that the 2d Sox run was from a Casas double, a grounder moving him to 3d base, and a wild pitch bringing him home. Casas does not score without that WP because the next batter walked and then Rafaela flied out for the third out.
So, basically, you and others are pissed at Cora for sending Pivetta out to pitch the 6th when he'd thrown just 70 pitches and had a seamless (3 up, 3 down) 5th inning.
And you deliberately downplay the fact that the Sox collective lineups for the doubleheader drove in 1 run in game 1 and another run in game 2.
Cora is not the problem for this year's Sox. He was terrific in the 2018 season, the single best Sox season ever, and pretty terrific in the 2021 season when the Sox were without a bunch of the stalwarts from the 2018 team--Sale, Price, Porcello, Kimbrel, Mookie, Benintendi, JBJ, Holt, Moreland, et al.
In fact, I would argue that the 2016 and 2017 teams both had more talent than the 2021 Sox team, but they didn't have Cora managing and were smacked down in the ALDS, 3 games to 0 both years. The 2021 Sox had no closer for the postseason, but still beat the Yankees in the wild card and the 100 win Rays in the ALDS, 3 games to 1, before losing to the Astros in the ALCS.