Syncthing does that job (and many more).
Discussion
With respect, syncthing is a PITA an no average person is ever going to use that, imo. The average user thinks, “what can solve this problem.” They don’t think, “what set of different apps can I use to work together to partially solve this problem in an iffy and unreliable way?”
As someone who has spent years doing the latter with SO many different tools, I despise how annoying and unreliable it all is. No chance it ever becomes broadly used by others.
If you're not using Syncthing to backup your phone, are you using the cloud?
I don't think the average person is even using a password manager.