Install vanilla LineageOS or GrapheneOS with no GApps. Then install Signal from https://signal.org/android/apk/
Unified Push, which works flawlessly on Molly, could easily be implemented in the regular client.
Signal works without GMS or any alternative, at the cost of more phone wakeups. This is much more preferable to everyone whose WiFi or data service you use see you connect to "push.myownname.com", or for you to rely in some rando gatekeeping your message delivery.
Mozilla has one. Hell, Signal _themselves_ could host a UnifiedPush server. Not an excuse to say 'you use Google or our app uses 10x the battery'.
I bought a PinePhone, so I definitely know what truly unoptimized battery life looks like, lol.
That being said, I've never heard this mentioned as a benefit of Signal, and I figured the main benefit was y'know robust and proven E2E encryption.