Mayor Adams has always had a startlingly over-casual attitude toward the appearance of corruption.

His mayoral campaign and administration have been dogged by federal investigations and press reporting of irregularities from the start.

But they’ve always been peripheral to his election and re-election platform: cutting crime.

The latest round of federal raids, at the homes of his three top public-safety officials, changes that, and thus imperils Adams’ only already fragile claim to mayoral success.

Last Wednesday, federal investigators executed search warrants at the homes of Police Commissioner Edward Caban, Deputy Mayor for Public Safety Phil Banks, and Tim Pearson, a top Adams aide in charge of migrant-shelter security operations (plus a couple of other City Hall high-ups, but that’s already enough).

No one is under indictment, and the feds often mess up.

And yet: Nobody is shocked by this development, and this cynicism is entirely Adams’ fault.

Upon taking office in 2022, he tapped Banks — even though a decade previously Banks, then the top uniformed police official, had been caught taking high-dollar gifts from influence peddlers. (Banks wasn’t charged with a crime, but others were, and were convicted.)

The Post’s editors warned that hiring Banks would “hobble” Adams’ “war on crime.”

Pearson, too, is cavalier with the rules: Early on in the Adams administration, he tried to keep both his new City Hall gig and a casino security-chief job, even though City Hall helps regulate casinos and will have a role in awarding new casino licenses.

Then there’s Caban, who takes an awful lot of luxury trips paid for by third parties, including the government of Qatar, which harbors Hamas leaders.

As a younger cop, Caban was once punished for lying about his shifts and for using his government car for personal use.

Because Adams didn’t heed early skepticism about this crew, his entire public-safety leadership infrastructure is now distracted by a sweeping federal investigation.

And that’s when Adams’ only credible argument for reelection — that he’s cut crime — is already weak.

After the federal raids last week, Adams went on FOX 5 to tout his “decrease in crime,” and vowed that “we’re gonna continue to drive down crime.”

He dismissed the fatal gang shooting at Brooklyn’s West Indian Day Parade over Labor Day weekend, saying that at the parade, “you saw police officers, community groups, crisis management team, you saw an amazing response.”

But crime is actually not consistently down during Adams’ administration.

The numbers are now out for the year through Sept. 1, Adams’ third mayoral summer, and the last summer before he has to win a June primary next year.

Yes, felony crime is down 2.4% from last year, and that puts it down 2.4% from 2022, as well.

But this flat trend leaves felony crime 33.8% higher than it was in 2021, the last year of the previous administration.

We haven’t seen felony crime rates this high since 2006 — and back then, crime was steadily falling.

The tiny little declines Adams can tout aren’t the reversal New Yorkers expected when the elected him in 2021, especially since robbery and felony assault rates keep going up: Both have risen this year.

Adams has mostly done well directing the NYPD to focus on gang murder — murders are down 25% since 2021.

But they’re still 17% above the record lows New York achieved between 2017 and 2019.

Adams keeps talking about how subway crime is down — but the city has suffered nine subway murders this year, three in the past two weeks.

That puts New York on track to exceed the 11 transit murders clocked in 2022, a level not seen since the city started cutting underground crime in the early 1990s.

And Adams is in denial about the level of disorder on city streets — including disorder spilling out from poorly policed migrant shelters in core Manhattan.

So it’s not a great time for Adams’ hand-picked public-safety chiefs — all of them — to be worried that they, themselves, have been caught on the wrong side of the law.

In tolerating all his deputies’ low-level sins, Adams seems not have heeded the rule of broken-windows policing: Small crimes, if not kept in check, risk leading to bigger crimes.

Adams’ failure to impose discipline at City Hall threatens his already fragile — and in some areas, nonexistent — public-safety improvements for all of us.

Nicole Gelinas is a contributing editor to the Manhattan Institute’s City Journal.