Just want to comment more detail on the solution if others have this issue.
My setup: Pixel 8, running Google Messages in a secondary profile here. I tried to keep all the google activity in the secondary profile. Google messages is the default in all profiles and stock app is disabled.
Result: If Google play service is disabled in Owner or other profile, Google messages will send constant nuisance notifications that it cant run without the service. The 2 fixes I could think of:
1) Mute Google messages notification on owner and let it ERR in the background
2) Enable Google play services in a neutered state in Owner profile by removing all permissions
Opted for 2 because I just didn't know if 1 would have any other issues or drain battery. Texting is working now