Look, I try to avoid bringing up nix in unrelated conversations. But.

The only two options I have is a) do a factory reset and reinstall software from scratch and spend time configuring things again, or b) live with all of the extra garbage that has been excreted by the software on my systems just so that I can keep the data that I actually want to keep.

NixOS solves this.

My ideal system would separate data that was written because of me (non-default config values, bookmarks, etc) from documents etc made by me, from garbage that the program wants to write that I absolutely do not care about and do not want to know about.

And NixOS with https://github.com/nix-community/impermanence does this, forcefully. Actually normal nix might solve it depending on how far you want to go.

Again, I wouldn't usually try to evangelize it, but you have described your ideal system, and it exists.