Looking at your error it’s because Rsync is erroring.
I’d starr by testing Rsync with an individual text file saving to /dev/dm-0 and see what error is returned.
Timeshift is good but it basically is just a tool to use Rsync to save a copy of your system folders (or other folders if you wish).
Rsync needs to be able to read the source and write to the destination, so I’d start with testing that Rsync is able to do that.
Given you’re using an encrypted partition it’s possible you’re trying to read/write to the wrong locations. You’ve provided device UUIDs but you’d probably actually need to be backing up the mounted decrypted locations? I.e. the root file system / will actually be a mounted location in your Linux set up, probably under /run, with symlinka pointing to it for all the different system folder. Similar for /home/ if you want to back up personal files.
The device UUID would point to the filesystem containing the encrypted file (managed by LUKS) which will have very limited read/write permissions, rather than directly to the decryoted contents / or /home partitions as you’d expect in a normal system. In particular if /dev/dm-0 (looks to be an nvme drive) is an encrypted destination then really you also want to be pointing directly to it’s decrypted mounted location to write your files into, not the whole device.
Edit: think of it like this, you don’t want to back up the encrypted container with Timeshift, you want to back up the decryoted contents (your filesystem) into amother location in your filesystem (encrypted or decrypted). If the destination is also an encrypted location you need to back up into its file system, not the device where the encrypted file sits. So use more specific filesystem paths not UUIDs. That would be something like /mnt/folder or /run/folder not /dev/anything as that’s hardware location, and not directly mounted in an encrypted filesystem unlike how it can be in a non-encryoted system.



I’ve tried Arch - it allows you to make a system that is exactly what you want. So no bloat installing stuff you never need or use. It also gives you absolute control.
On other distros like Fedora, you get a pre configured system set up for a wide range of users. You can reduce down the packages somewhat but you will often have core stuff installed that is more than you’ll need as it caters to everyone.
Arch allows you to build it yourself, and only install exactly the things you actually want, and configure then exactly how you want.
Also you learn an awful lot about Linux building your system in this way.
I liked building an arch system in a virtual machine, but I don’t think I could commit to maintaining an arch install on my host. I’m happy to trade bloat for a “standard” experience that means I can get generic support. The more unique your system the more unique your problems can be I think. But I can see the appeal of arch - “I made this” is a powerful feeling.