Yesterday I downloaded Spotify again for the first time in a year and found the same issue again. However, now when I drag the window across monitors, the icon follows suit in the taskbar. That's different from a year ago, at least.
We've done some investigating on this and we’d really love to help with this but are unable to as it's to do with Windows rather than Spotify. We recommend getting in touch with our friends at Windows. They’ll be able to provide you with the best possible support.
Sorry we can’t do more, but let us know how you get on. We’ll be right here if you need any further assistance.
Help others find this answer and click "Accept as Solution".
If you appreciate my answer, maybe give me a Like.
"Kindness is the language which the deaf can hear and the blind can see." - Mark Twain
I DM'd this support account yesterday and @SpotifyCares asked the first relevant question anyone at Spotify has ever bothered to ask in at least 200 days: "What are your taskbar settings?"
Just 20 more questions, I'm sure, and Spotify will be able to muster:
>Oh, so this bug is with two monitors. We did not realize that from the first report. So, Spotify's final recommendation is to contact your monitor manufacturer (preferably the manufacturer who made the monitor where the icon does not appear) and then your local electrical utility for an appeal. Barring a resolution from them, my research shows your city council has the final appellate jurisdiction, unfortunately. Bugs about two monitors are pretty much beyond our control.