You can set up your watch using a phone, and then turn the phone off and the watch still works. What doesn't work is SMS messages from non-apple users, because they are forwarded from the phone.

I set up my daughter's Apple Watch SE which we got her because phones are depression machines for teen girls (according to the Biden controlled MSM anyway) and I just set it up using my backup phone. I then backed up her setup, restored my setup, and when I need to update her watch or do something else administrative I just restore her backup to the phone, do what I need, then restore my backup to the phone, ready to fill in at a moment's notice if my phone needs to be repaired or gets lost or whatever.

I also take calls on my airpods connected to my watch pretty frequently because I exercise without my phone. I've never really had a problem with it.