You could also try installing from a deb file:
Hi, I've tested it myself that Spotify option, also not working here. I would say it's a gnome issue, considering you are using the default gnome. The strange thing is that other apps work fine, like dropbox or flameshot
more info here Re: Cannot minimize to tray on Linux - The Spotify Community
I can minimize my Spotify (apt install) without any issue.
I use GNOME desktop in Zorin 16.
ditto. But I also uses apt get to get it to avoid snap/flat
Has the OP removed the Snap package prior to installing it via apt?
Sorry, maybe I was not clear enough, minimize works fine, but it doesn't move to system tray when you close the window. Btw, I have the .deb installed, not Snap nor flatpak pkgs
Did you add Spotify to your Favorite?
If I add it to Favorites what happens is the Spotify icon stays in the left side of the taskbar but not running. Going into the system tray, the icons in the right end of the taskbar, means spotify should be running in the background without the need to have a window active, pretty much like windows or mac Os.
I am using Zorin16 Pro with a Mac like design.
It is difficult for me to visualize what you have described.
Any chance for the screenshot?
In my setup, the left end of top bar shows whatever the app my mouse is focusing.
When I am in Firefox, it shows Firefox icon, when I am in Spotify, it shows Spotify icon, etc.
Is it Zorin Core or Lite you are using?
16 Core, default gnome, nothing fancy 
I am on Zorin 16 Core, but installed XFCE desktop. I do not use Gnome.
That's what I was about to say, he's a xfce guy. Actually i'm really close to revert to xfce as well. I decided to give a chance to gnome for the z16 release. Dont worry with this spotify issue, it's nothing major but it would be nice it could be running in the backgroung, like Rhythmbox does in Gnome. I close the window and the sound keeps playing, I do the same in Spotify and it shuts down.
There should be Zorin 16 Lite released "soon".
I am eager to upgrade my dual-boot Acer Aspire which is currently running Zorin 15,3 along with Windows 11.
Good point! I will hang for some more time then. 
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