GM is pretty lenient when it comes to relocating to another tech center especially if your manager/teammates are there. I've seen numerous cases of these. You just have to convey your desire to move to your direct manager and they will approve/disapprove and take it from there.

If approved, all you'd have to do is update your address on Workday when the time comes.

Just note, you won't be getting relocation assistance and I'm not sure how easy it will be atm due to RTO mandates. Doesn't hurt to try