Funny you should ask this -- I was just coming here to ask people if they have any tips about it.
I have two user accounts on my Mac. One main one which is signed in with the same Apple ID I use with my iPhone and my AirPods Max, and a secondary one I use for work, signed in to a different Apple ID.
In the primary account, the APM pair up and work fine. When I log into the secondary work account, they unpair immediately and don't show up in Bluetooth or anywhere else. It's incredibly frustrating. The only way I've found to get them to work at all under my work account is to actually reset them and re-add them to the computer -- at which point they get renamed "[work account]'s AirPods Max" and are no longer discoverable by my iPhone or my main Mac account.
Super, super frustrating. I get that they don't want any random Mac to be able to hijack your headphones, but surely there's a better way to do this. Especially for $550 headphones.