I have installed the app twice now on my Windows 11 system. The thing works beautifully after installation. System/sounds is showing what seem to be all the right parameters. The app is in the run at startup menu. When I reload my system no system sounds or Spotify. What a pity, it is a good enhancement.
I pinned my standard troubleshooting list to the top of the forum.
Also, there are two ways to use Spotify on a computer: via your browser, and via the standalone app: have you tried both?