Good. So you’ve confirmed that games can and do run on your system, both natively and using proton.
Next, I would try deleting the corresponding compatdata and shadercache folders for the games, to reset the games prefix and shaders. These are one folder up from the folder where the actual game files are, and the folders within have numbered names that match the ID of the game. (Which you can see in the update tab in game properties).
Simply delete the correct folders and steam will redo the proton setup for a game and recompile the shaders.
On a sidenote, I recommend installing proton-ge-custom from the AUR, it installs, keeps up to date, and makes available proton GE for you to use in steam and heroic, should you ever need a version with fixes that valve proton doesn’t come with.