@Vlad-Nirky Hmm, not sure. Running adb root for me gives error message adb: unable to connect for root: closed, but I can use sudo inside adb shell: using that would probably let me get a step closer, by allowing me to copy data to an SD card for instance. The problem is my computer isn't an adb client so I can't just use my phone as a host and run adb root on it.
Going back to the module installation, I should definitely look into that (or whatever procedure I need to enable adb root), as it sounds better than the whole hassle of the SD card (which funnily enough is one of TWRP's limitations).
[UPDATE]
I've been told by an admin of UT's Telegram group that adb root simply hasn't been added to UT. This shouldn't be a problem, as utilities like rsync and scp, which are meant to work over a network, can be set up to work over for example USB (or maybe even Ethernet, don't know which would be faster or in what scenario).
I may test backing up and restoring a Waydroid container with SD card, SSD and PC (using sudo on UT so that I have the priviledges to save all kinds of rights).
I've been told by the same admin this works: therefore, all that's left is finding the right command for the job, so that it restores a Waydroid container to a working state (although this procdeure should be applicable to any app or user data or configuration).