Hi, I am that Gnome user,
I was trying out ActivityWatch yesterday for the first time. I noticed that in the documentation you stated that the system tray icon doesn't work but it appeared to. I did some research and it was because when I installed Steam (that has it's own system tray menu) it had installed AppIndicator and KStatusNotifierItem Support, which let all of my system tray applications work again. Everything in the system tray works as expected (after a reboot) so I would like to see this in the documentation to help other people out.