100% CPU use doesnt make sense. RAM would be the main constraint not the CPU. Worth looking into - maybe a bug or broken piece of software.
Also the DE may he more the issue than the distro itself. You could install an even more lightweight desktop environment like Open box. Also worth checking whether youre using x11 or Wayland. Its easy to imagine Wayland has not been optimised or extensively tested on something like your device, and could. Easily be a random bug if the DE is pushing your CPU to 100%
There are super lightweight distros like Puppy linux.



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 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 of /dev/dm-0 is an encrypted destination then really you want to be pointing directly to it’s decrypted mounted location to write your files into, not the whole device.