The broom that swept out the last Giants’ regime just came out of storage to scrub Logan Ryan.

In a surprising move Thursday that had almost nothing to do with salary cap savings, the Giants cut Ryan and ushered in a seismic change in locker-room leadership. Ryan was a co-captain, started 30 of the past 33 games at safety and wore the defensive play-caller’s helmet at times.

Whereas the rest of the Giants’ offseason moves have been convincing injured players to take pay cuts or swapping dead cap space for bigger cap savings, the Giants saved just $775,000 by cutting Ryan. That’s about $65,000 more than a player earning the league-minimum salary.

The Giants chose not to have Ryan at the cost of $11.45 million in dead cap instead of keeping him at $12.225 million. It reportedly saves about $3 million in cash from the portion of his salary that would’ve become a guaranteed payment later this week.

If the Giants had designated Ryan as a post-June 1 cut, it would’ve cleared more cap space this year but left a $3 million hit in 2023. This way, the Giants are off the hook next year.

One source close to Ryan told The Post that, while the New Jersey native’s preference was to stay with the Giants, he is welcoming an opportunity to chase a third Super Bowl ring rather than spend his age-31 season in a teardown rebuild. He wrote on Twitter, “Thank You NY Captain Log Out,” with heart and call-me emojis.

The Giants have safeties Xavier McKinney and Julian Love on rookie contracts. Jabrill Peppers is a free agent coming off a torn ACL.

Ryan’s leadership style was bred with the Patriots, and he was former head coach Joe Judge’s locker-room translator. The Giants fired Judge, lost defensive coordinator Patrick Graham to the Raiders and decided to make a clean break by cutting Ryan even though new head coach Brian Daboll and Ryan were together (on opposite sides of the ball) for four seasons in New England. Daboll will have his own mouthpiece.

“Nobody in the locker room had issues with Logan and everybody respected him, not just because of what he said but what he did,” one Giants teammate said. “He works hard. He was always on time. He coached up young guys to do extra if need be.”

Ryan had the best year of his career as a slot cornerback with the Titans in 2019. He remained unsigned as a free agent until August then played so well on a one-year prove-it deal that the Giants signed him to a three-year, $31 million extension on Christmas Day 2020.

But Ryan didn’t make nearly as many game-changing plays last season and slipped to the No. 60-rated safety in the NFL by Pro Football Focus. Ryan’s versatility to play deep or in the box seems to fit new defensive coordinator Wink Martindale’s system — and defensive backs coach Jerome Henderson was retained — but it seems clear that the player evaluations done by the coaching staff and general manager Joe Schoen weren’t returned in Ryan’s favor.

It wasn’t the change to the secondary that everyone was expecting. The Giants can save $12 million against the cap by trading cornerback James Bradberry, but teams are reluctant to offer draft compensation as they wait to see if he will be released.

The Bills are in the market for a veteran cornerback, according to ESPN, which makes sense unless that is general manager Brandon Beane trying to heat up the Bradberry market for his protégé Schoen.