I can confirm that this bug is still present in Spotify 220.127.116.119 on an iPhone SE with iOS 13.3.
I strongly believe that this a race condition in the Spotify app happening when playing music with the loudspeaker of a mono iPhone (before the iPhone 7) and then switching to AirPlay 2. I also think that this is not a problem of iOS, as YouTube and Apple Music do not show this problem.
Spotify's support helped me reproduce the bug with their own test Spotify account and playlist, with "Mono Audio" disabled and "Balance" centered. This can also be tested easily with the song "You Never Can Tell" from Chuck Berry with the piano coming only from the right loudspeaker.