The network icon usually contains controls for connecting to and disconnecting from networks, which are obviously useful.
> I guess you'd have to have used Windows to miss it then.
I don't understand what you mean by this. For most of the past 30 years, every major OS had something analogous to a system tray. Win, Mac, KDE, Gnome all had icons next to the clock, that gave access to software running in the background or system functions. Virtually all still do, Gnome (apparently?) does not.
I find it deeply implausible you've never seen or interacted with a system tray.
Well, I've probably seen it, but it's not really been something I've paid attention to. Except of course maybe the clock, which is present in plain ordinary Gnome whether it has a "system tray" or not.
It's mainly to let you know that theres a program that's running in the background but not open so you can get to it easier. For example, I know a lot of chat clients will live in the system tray so they can show a little dot with your missed messages. Also, VPNs specifically use them to provide easy dropdown menus to change things like server location
Why would I care about what the network is doing?