Linux

Regardless of what technical solution you decide to rely on, e.g borgbackup, Synchting or rsync, the biggest question is "what" do you actually need. You indeed do not need system files, you probably also applications (which can fetch back anyway) so what left is actually data. You might want to then save your ~ directory but that might still conflict with some things, e.g ~/.bashrc or ~/.local so instead you might want to start with individual applications, e.g Blender, and see where it implicitly or you explicitly save the .blend files and all their dependency.

How I would do it :

• over the course of a day, write down each application I'm using, probably a dozen at most (excluding CLI tools)
• identify for each where data is stored and possibly simplify that, e.g all my Blender files in a single directory with subdirectory
• using whatever solution I have chosen, synchronize those directories
• test on the other device while being on the same network (should be much faster and with a change of fixing problems)

then I would iterate over time. If I were to often have to move and can't really iterate, I would make the entire ~ directory available even though it's overkill, and only pick from it on a per needed basis. I would also insure to exclude some directories that could be large, maybe ~/Downloads

PS: I'd also explore Nix for the system and applications side of things but honestly only AFTER taking care of what's actually unique to you, i.e data.