Syncthing is my answer though I appreciate it doesn't get to the root of your question.
There are local backups that include your system settings, text messages, contacts, call history and (optionally) apps. The one thing I want is the ability to pick a directory for the local backup so I can make it work with syncthing without jumping through hoops.
It's also compatible with Nextcloud and WebDAV if those are options for you.
Syntax-wise, it's meant to be identical. I got on board when they were the only ones that enabled rootless (without admin privileges) mode. That's no longer the case since rootless docker has been out for a while.
I'm personally a fan of the red hat docs and how-to's on podman over the mixed bag of tech bro medium articles I associate with docker.
At the end of the day this is a bit of a Pokemon starter question. If your top priority is to get a reasonably common and straightforward job done just pick one and see where it takes you! :)