Connect Apple 27 inch monitor to MacBook Air 2022 M2

A search of MacTracker for that model number indicates that this is a standalone 27” Apple Thunderbolt Display. Apple sold variants of this display between mid 2011 and mid 2016.

If that is correct, you need an Apple Thunderbolt 3-to-2 adapter. You may also need a Thunderbolt 1/2 cable if it turns out that the permanently attached one is bad or flaky, and that running a cable to the monitor’s Thunderbolt daisy-chaining port is the only option for saving the display.

You don't.

The iMac cannot be used as a monitor for another computer.

Once upon a time this was a feature, but it's been dead for over a decade.

Aaaaannnnd I'll be apologizing now for misreading your post as a question regarding the 27" iMac instead of the 27" Thunderbolt monitor that @Servant of Cats has identified. Sorry.

Fortunately, you're on the right track now. 👍🏽