I’ve also been distro-hopping, but settled on NixOS. I find it very clean, you know exactly where your (system-level) configuration files are (…and could even manage user-level config files using home-manager). There is a stable branch, which is, well, stable. And even if it wasn’t, you can rollback the system at any point, which is trivial (just select a different generation during boot).

One of the biggest advantages for me is universal reproducible working environments. Using Nix+direnv, I can lock all tools (make, gcc, JupyterLab, Python, Julia) that I’m using in a project to specific versions (and upgrade/rollback). I can install programs/libraries in a nix shell and they will be removed on the next garbage collection. Upgrades are extremely safe: I once had a problem with RAM that corrupted a lot of my files during an upgrade. Nix can detect and repair this.

Downside is that Nix doesn’t follow FHS, so some programs need a little help, for example by Nix’ steam-run.

On my NixOS, nix sets the environment variables XDG_DATA_DIRS, XDG_CONFIG_DIRS, etc. Maybe these contain what you‘re looking for? Do you have a path ~/.nix-profile/share/applications?