How does one remove a device from your own list of devices so as to give it to someone else?

Recently I purchased a new macbook pro (16"). I'd like to give my old macbook pro (13") to my mother, who currently uses an old 2014 macbook air. Upon doing a factory reset I've noticed I'm unable to setup the old device in her name with her account. The migration assistant app doesn't recognize her macbook air so as to import her files. When I attempted to do a clean install with her apple ID, 2FA would ring to her phone, but the code, when input into the air, did nothing.

Based upon further research, and general observation, the old macbook pro 13" is still listed on my list of devices. In fact, the new 16" doesn't yet appear in my list of devices. I've also heard that a simple factory reset doesn't wipe out your account information or sever the tie of the device from your list of devices. It's apparent that the apple ID is tied to the logic board of the macbook pro 13".

How would I resolve this? Does this scenario necessitate a trip to the Apple store? I hope not!

Thanks in advance to any insight you can provide!