Kinda lame that the only way to get the Android app is through Google Play, they don't have apk's on their website or github. I mean you can compile it but who wants to do all that to try out an app?

from their github issues: Release app on F-Droid

glouvigny (developer):

What Google or Apple for iOS will see on their servers is an encrypted payload, the recipient device identifier and the moment the push has been sent. However, on the privacy level Berty's relaying servers are able to determine both ends of a message (the originating IP address, the target device). I'm not sure anything can be done around that, apart from using your own service or disabling push notifications altogether.

We also plan to let users host their own push server or chose a trusted third party, however it might trigger some warnings on Android. I don't remember the exact message but it be something like "Disable battery optimizations for the app".

Anyway, our main goal is to provide an easy to use app, with as few configuration as possible, that's why we are prioritizing development of push via Google over self-hosted solutions.

I'm not a fan of a "decentralized" messenger that relies on Google for push notifications.