An easy option is to add the data folders for the container you are using as a volume mapped to a local folder. Then the container will just put the files there and you can backup the folder. Restore is just put the files back there, then make sure you set the same volume mapping so the container already sees them.

You can also use the same method to access the db directory for the migration. Typically for databases you want to make sure the container is stopped before doing anything with those files.

Anything you want to back up (data directories, media directories, db data) you would use a bind mount for to a directory on the host. Then you can back them up just like everything else on the host.

All your docker data can be saved to a mapped local disk, then backup is the same as it ever is. Throw borg or something on it and you're gold.

Look into docker compose and volumes to get an idea of where to start.

You would leave your plex config and db files on the disk and then map them into the docker container via the volume parameter (-v parameter if you are running command line and not docker-compose). Same goes for any other docker container where you want to persist data on the drive.