I recently migrated to a degoogled ROM and since many apps use google for push notifications, I've just been going without. And JTS honestly been quite freeing. If someone needs a quick response they can reach me on signal.
We are specifically talking about push via GCM / Apple here. Afaik signal opens a websocket in the background if GCM push is not supported. Or at least that’s how it worked a few years ago.
Google Cloud Messaging features (push) only work when you have gapps installed or use an alternative implementation like microg.
I assume that whatsapp also has some kind of fallback strategy built in.
I prefer Session for messaging and for family I ask them to reach me on Telegram FOSS.