I have the same issue. Looks like Spotify shuts volume after using some other apps with it's audio (e.g. youtube in safari) and then playing again on Spotify. So that's an easy bug to reproduce. should be definitely fixed.
Same issue with the two different sets of bluetooth headphones I have. The song bar will start moving when I click play, but no sound, and the blue bar will drop down saying there was an issue playing the song. No problems with playback with other apps, just Spotify.
Restarting the headphones or disconnecting and reconnecting them works.
When trying to play Spotify the sound on my MacBook Pro Catalina 10.15.4 keeps going off and back on. All up to date software. Tried restarting spotify and Mac but issue ongoing.
Same issues when using Beats or MacBook speakers. Sound level show they are up. I can adjust the sound (when it plays) by using the Command and up arrow (or down arrow) or go in to settings, or use the slider on Spotify bottom right BUT the SOUND KEEPS GOING OFF AND ON!
When it goes off there is a message at the top in a blue bar that shows up and says "Can't play the current song."
This has been an issue for YEARS with the desktop version of Spotify. This is definitely a software issue for Spotify that they still haven't addressed after all this time. The alternative would be to use their web player. Spotify's desktop app is junk.