I run gnome on all my machines with displays, for many years now. I never paid much thought to what "AppIndicator" is, but I've always used what I believe you're calling "systray", if I understand correctly?

I have temperature and network gauges on the top right next to my battery/audio/WiFi indicators. My work laptop (Ubuntu) has indicators up there for Livepatch and Mattermost, or are these not the same thing?

As far as I recall, I've not had to do anything particularly special other than install the extension for the thing I want, Freon etc, and the Livepatch and Mattermost ones were just there whether I wanted them or not.

It's possible I did something when I setup Gnome on my personal laptop (Arch) but other machines are running Ubuntu and I think it just did this OOB.