Omniplayer uses an old client SDK which is now outdated. It does still work if you have it in your application, but Spotify does not issue any new API keys for new applications anymore.
Even though promised by Spotify years ago, no replacement for that SDK has been released since years ago. In fact, there is no SDK/API for Windows desktop apps at all at this time, only for iOS, Android and web-based applications:
See for yourself here: https://developer.spotify.com/documentation/
So it’s technically impossible at this time.