Do I really have to jump to a new compositor/window manager to get this? Seems like I should be able to query the state of my desktop without doing that. :(

In theory if GNOME exposes enough API surface then sure you can write a plugin to do it. I'm rather under the impression that GNOME is not particularly friendly to that kind of customization work, though. Perhaps it's better these days; I haven't paid it as much attention since jumping ship. It is entirely possible that it would be less overall work to switch to a window manager that enthusiastically exposes all the API surface you could ever ask for, but don't let that stop you from looking into it.