I'm on cachyos Wayland (hyprland) and none of the GUI options worked for me, including the flatpak. The AUR protonvon-cli-community worked out of the box though.
I don't know why it didn't work. I just tried all the options until something worked and didn't care enough to try to fix the options which didn't work.
If I'm reading that correctly, yeah all you should need to do is install the AUR package. 1.1-1.3 in that section are different options that don't depend on each other.
Reminder that proton doesn't give a shit about linux support (for any of their products) and you will be better served in the long run supporting a company who supports you. Not one who uses privacywashing as a sales tactic but is perfectly okay ensuring their products only work (full feature support) on corporate spyware OSes. This creates yet another barrier keeping their customers on w1ndows/mac which completely defeats the purpose of using proton services if your OS is sending everything to gemini anyways.