This, or the Tray Icons: Reloaded extension for GNOME, which adds the Steam icon to the tray bar. From there, you can click it and it shows a list of the installed games.
If you are new to Linux, GNOME has quite a different feel from your usual Windows flow. I personally love it and would never swap back.
(Off-topic, but If you would be interested in a gaming-oriented distro, I would recommend Nobara Linux - the official version looks fairly familiar for Windows users and it also comes with a bunch of gaming-related stuff preinstalled like Steam, wine dependencies, mesa drivers for AMD, etc)
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.