So the problem is basically in the title. Now obviously this may be better suited for the OBS forum but I figured I would still ask here. When using the Audio Capture feature on OBS it simply won't capture the audio of Cider.

It's because of the DRM. So you can't stream or record copyrightes songs.

GameKuchen is correct here.

Cider uses DRM due to how MusicKit handles audio.

If you’d like to capture Cider’s audio thread, you’ll need to use an OBS plugin or something to capture it from the actual WebView2 runtime.