Currently you can only try it by building it yourself, instruction here. https://codeberg.org/solver-orgz/treedome/src/branch/master/docs/building.md
But .deb and nixpkgs update is planned to follow suit though! You can also try an outdated one in https://aur.archlinux.org/packages/treedome-bin.
Tell me what you think about it!
On desktop it’s the matter of extensions, so following your idea keepass or pass won’t make a good password manager without a third party browser addon