The choices soon boil down to what compromises you are willing to make, I guess.
And, as such, the decisions made around private use will probably differ from this made around my music. The goals are different, so different compromises will be made.
I must admit - I'd not thought about using messenger in Brave. I am a Brave user, and - to be honest - most of the stuff that gets posted to messenger isn't time critical - it doesn't need to be on my mobile. Folk can still SMS/call for anything urgent. (Or use Signal, indeed)
More food for thought. This is A Good Thing - cheers!
The Messenger app will still fingerprint your device. Once connected it has access to your MAC address and also triangulation via cell towers and even WiFi routers (assuming most are not configured to send a fake location).
With Brave Shields and fingerprint protection, messenger doesn't get access to those and can not fingerprint your device. Unless you explicitly allow it.