Elected officials aspire to be admired, respected, feared, beloved — but failing that, you’ve got to at least be noticed.

As New York’s movers and shakers get back to their fall routines, Mayor Adams is sliding into the worst fate of all: being irrelevant and . . . ignored.

Last week, at a marquee event attended by the city’s real-estate, business and political leaders, the mayor was mostly noticed (by me) for his total absence.

The governor showed up and made a serviceable speech. Another top pol phoned in a video address.

But the mayor was . . . nowhere.

Yes, he had COVID, but nobody offered an anodyne “We are sorry Mayor Adams can’t be with us, but he offers his best wishes.”

At a similar event three years ago, ahead of his general-election victory, Adams was the star of the show.

Similarly, a business bigwig was recently musing about how East Midtown executives are really upset about the state of the Roosevelt Hotel.

It’s easy to see why: The back of the building is covered in graffiti, dirty hotel laundry spills out of a giant streetside container, a guy frequently sits outside cutting people’s hair for a few bucks, and general chaos reigns (no cat eating, though).

But the bigwig wasn’t interested in how to get Adams to fix it.

Rather, this person was wondering if there’s a way to address the issue without having to go through City Hall — an exercise he dismissed as entirely hopeless.

(When people start scheming about how to shame the government of Pakistan, which owns the hotel, into taking action, you know that things are pretty bad locally.)

Nobody is surprised at the resignation of former Police Commissioner Edward Caban, amid the feds’ investigation of what is emerging as a pay-to-play shakedown scandal involving two separate families, the Cabans and the Bankses. (Caban says he’s not the target of the investigation.)

And nobody is sad to see him go: Whether he did anything wrong or not, he wasn’t much impressing anyone.

Every administration has its scandal — a commissioner who has to quit under a cloud, a campaign irregularity.

But this administration doesn’t even appear to grasp the seriousness of its predicament.

Exhibit A is how Adams still keeps top aides Phil Banks and Tim Pearson close to him. He appears to be helpless without them.

Plus, this administration seems to be making no progress on any front.

On paper, Adams and his openness toward looser zoning rules and other “city of yes” proposals is good for business.

On the streets, it’s another matter.

Adams can rattle off crime and economic-recovery statistics, but if you’re a top executive, you don’t pay much attention to that stuff. You do know if your wife is too afraid to take the subway home from a play.

And you can sense, as a New Yorker, that you are . . . embarrassed.

Just walk down Sixth Avenue in the afternoon rush: A man blasts ear-splitting amplified music and bangs on some drums just inches from pedestrians.

Another man advertises his marijuana-delivery business via a megaphone outside the doors of Whole Foods.

Vendors take up half the sidewalk selling knock-off LV bags. E-bikes zoom every which way (if there is a right way to ride illegally on the sidewalk).

This embarrassment is compounded if your business, or your summer vacation, has taken you overseas.

London, Paris, Brussels, Stockholm, Hamburg, Tokyo — no other global city puts up with this level of easily fixable disorder.

If you’re a bloodless executive, Adams is a write-off.

Sure, you’ve got to keep paying him for a while (Adams’ fundraising is doing well).

But like any once-promising employee whom you can’t fire immediately for whatever reason, you can just . . . ignore him. Freeze him out.

After multiple overtures and multiple second chances, he’s proven himself not useful, and he’s thus not worth wasting time on. It’s nothing personal; it’s just human resources.

The question for voters is, who’s next?

The crop of challengers for next year’s primary election is hardly inspiring: left-wing city comptroller Brad Lander, another two equally left-wing state lawmakers, plus Scott Stringer, a former comptroller whose mayoral campaign excited no one last time around.

So for now, the position can be advertised as open: Who wants to be the next pragmatic, business-friendly mayor, the guy Adams was supposed to be?