Thank you for your comment. Since I deactivated Google Play services, I don't get notifications on many apps. I didn't know there were alternatives. Unfortunately, the app server must be compatible, but if I can have it at least for Telegram with this fork, it would be a good start. I'll take time to compare the different alternatives and see if other push servers are compatible with more apps.
For what I understand, there are self hosted push servers, like NextPush that works on Nextcloud, and some that provide you a server, liked ntfy. For the latter, you have to check the privacy policy to see if it's better than the default Google firebase server.
It doesn't interoperate well with FOSS software like K9 and Thunderbird.