This is the only addon I've found that actually works on desktop. I use Second Sidebar for Firefox (check GitHub), and I pin YouTube Music as a web panel. I'm normally forced to use desktop view which sucks because of the small space. But if I use mobile view, playback always stops. This addon worked like magic and YT Music hasn't stopped once since I installed it.

Also seems to work well on mobile too, but I mainly use it on desktop. Thank you to the developer!