I’d recommend installing the flatpak. Tf2 stopped working for me when I upgraded to fedora 38. The flatpak seems to fix whatever dependency issue is causing it. It also fixes portal 2 and Gmod cause those also stopped launching on f38.

Did you update your system other than your nvidia driver? Like from fedora 37 to 38

Don’t know if it’s the answer you are looking for but if when you install the game you click add application menu shortcut it will add it to the menu that opens with windows key. I have never personally used desktop shortcuts on gnome since it isn’t included stock.