I am not sure if this is correct functionality (which is why I am hesitant to mark this as a solution), but it seems to at least be a workaround for my issue. Turning on this widget allowed the Spotify widget/notification with playback controls to appear on the lock screen when music is playing, and for a short time after pausing a track. It also may have been turned off by default upon upgrading to Android 12.
Previously I had assumed that this was for Samsung's internal music player app only, which could be why it was turned off.
WORKAROUND Outlook search does not return results after upgrade to Windows 11. From there I went into the Lock Screen > Widgets menu, and turned ON the 'Music' widget. RESOLVED Outlook Search not showing recent emails after Windows update. However, I noticed when I swiped on my lock screen in a different way, the voice recorder widget appeared (which was a separate issue or so I thought because it kept doing this randomly). Then I turned it back on and restarted the phone with the same result. I turned it off and restarted, then tried playing music to verify (no controls present on lock screen). The feature you describe was on by default when I checked.
