I use Nautical. It will stop your containers before performing an RSYNC backup.
Yes the containers do need to be stopped. I actually built a project that does exactly that.
If you just need to backup Docker Volumes, I recommend Nautical.
You can use it to backup to an NFS share if you need to go between Machines.
Proxmox on bare metal. Then a TrueNas VM for storage. And a Ubuntu VM for containers.
I'm a little biased because I built it, but this is what I use.
I create backups of my Docker compose files and each container volume (these are done when the containers are stopped so no data is corrupted). Then I take those folders and send them encrypted to Backblaze using Kopia. Since it's just config files I am able to get away with the Free tier.
I also have my Docker compose files backed up in a private GitHub repo.
I feel the same way about not wanting to give my credentials out. I built a tool that takes all the Bank Expenses CSV exports and aggregates then I to a single CSV.
I don't know if that's what you're looking for, but it may help you out.
I actually Containerized one of my CRON jobs that used rsync to copy my container volumes to my TrueNAS server (link).
I think it's a good idea and you'll learn a lot along the way. Plus if you open source it then it will be way easier for people to get it up and running.