I use home assistant on gOS without play services and notifications via whatever means I have set up are instant and cause no significant battery drain.
Ill check to see what my setup is and report back.
Edit:
It is the persistant web socket.
Arguably the few websockets I have running for various apps use less battery than play services.
Home assistant barely shows up in my battery usage when in the background.
Its generally only corpo backed / play store apps that use play services for push notifs.
Signal > Molly in websocket mode solves the messenger issue.
Proton mail you may be able to set up with a third party service - from memory you cant use any other app.
Proton calendar should be local notifications? Test a reminder out like you did with the timer.
Emergency alerts are done through cell service and are unaffected.
Weather alerts will be dependant on what app you choose but if its FOSS you should be able to use ntfy and unifiedpush or local notifications.
Microsoft authenticator can live in the seperate work profile and realistically doesnt need push notifs - you will open it yourself to log in to shit when needed.
Call and SMS are unaffected - not push notifs.
Timers, Alarms etc are unaffected - local notifs.
Home assistant is designed to consolidate all the seperate parts of your smart home through integrations etc. Local notifications can be set up through the companion app for whatever your requirements.
I believe most of those red apps dont require play services to operate, mainly just for push notifications.
If I were you, I’d just use Aurora store in anonymous mode to keep those updated and use a firewall like rethinkDNS to block any potential trackers. I do this for my few apps that arent FOSS and banking etc.
Use web apps installed via vanadium for anything you can to delete the actual apps off your phone alternatively.
Theres a few websites easily searchable for replacing proprietary apps with FOSS you could explore also.