I just installed this game on my windows 11 PC, and since I've NEVER played any type of game like this on a PC before, I cannot seem to understand how to actually run it.
When I open either GOG, or Cyberpunk directly, I do not see a 'run' or 'play' button.
In GOG Galaxy, under the Downloads section of GAMES, at the far right of the screen for Cyberpunk 2077 is shown, there is a right arrow which when you hoover over it, it indicates 'play', but when you press it, nothing happens.

What am I doing incorrectly?

Go to your install directory, and look for Cyberpunk2077.exe
It's located in Cyberpunk 2077\bin\x64

If that file doesn't exist, or you're still getting an error, the game hasn't been installed correctly.
There also seem to be issues with this game and certain hardware configurations in Windows 11, but I'm still on Windows 10 (and I intend to stay there for as long as I can), so no personal experiences.