There’s a Home assistant desktop app that has a tray icon: Home Assistant desktop app (Electron )
Unfortunately it has not been updated to work with the new authentication system and the author has not been seen for a year.
Then there’s this: Mqtt Control - small mqtt client service to connect my windows based pc to home assistant
No tray icon (i think) but it may suit your requirements.
Edit: no that last one is only good for controlling the PC and displaying the PC stats in HA.