Did you verify the command was successful after deleting the Yay cache?
What is the output of ls -l /usr/share/applications/protonvpn.desktop
Can you try a new user to see if it fails to launch there too?
//EDIT: you can clean everything again remove it all, and use linus-aarhus repository to install it to verify it is not a build issue but a system wide issue.
After adding the repo to Pacman config, I guess simply do pacman -Syu proton-vpn-gtk-app