does genius bar fix broken macbook air m2 display onsite

No one here can answer that question except in the unlikely circumstance they happen to have had a Mac repaired at the same location you are planning to visit. Different Apple Stores have different repair capabilities, and it has been my experience that even stores that used to perform certain repairs in the past don't do them any more.

I suspect they will need to send it out, but that is literally no more than a guess based upon that experience. If they need to send it out, perhaps they can arrange to have the repaired Mac sent directly to you. I don't know.

In any event, start here: Official Apple Support. If anyone can provide a definitive answer, it would be Apple.

Here is another sort of reply. I have used portable Macs for over 20 years. Call me unlucky, but I have had to have at least 5 displays replaced. Every single time, I had to send it it. So, if you are headed for the "genius bar" with that goal, by a lottery ticket on the way, because you must be lucky to be trying that strategay.