This problem started when I was on Fedora 34 and continue to appear on Fedora 35.
When the system starts there always is this icon in tray that asks to reboot the system, but when i done that it won’t dissapear.
I can right click and end tray program, but it will appear again after next boot.
Update your system from the terminal… sudo dnf upgrade -y --refresh… After that completes, open discover and have it check for updates. If it doesn’t find any, the reboot prompt should go away. Same thing happened to me on gnome with gnome-software.