Update: Actually the contacts app doesn’t work right, can’t add a contact with Google Play Services turned off. Finding a non-Google contact app to use that will integrate properly with the rest of the apps is still a goal for me.
I have disabled Google Play Services, and find that everything is fine, so long as you take the time to disable the notices saying the app won’t work without Google Play Services. It says “Phone will not work without Google Play Services,” but that seems to be a lie, because if I ignore the notification, Phone (and everything else I can find) work just fine.
I have not found out how to do that across the boards. Seems to be you have to update it for each app individually. It seems the way to do that is to go to Settings –> Apps and Notifications –> Notifications –> See all from last 7 days –> tap the three dots menu, and tap ‘Show system.’ Then it’ll show the notifications from things like Sounds and Emergency Information, and you can toggle them off, mostly.
Except it won’t let me turn it off entirely for Phone and Emergency Information, but I can change the notification to Silent, and turn on Minimize, so it doesn’t go bing every five minutes, and the notice isn’t so big.
This is how it works in my Pixel 3a with Android 10 anyway. Could be different for other phones, and I can’t promise it won’t change.