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)