That sounds like a reasonable corollary to gtk_application_window_new, and should work work everything else.
But for PidginDisplayWindow, the activation uses pidgin_display_window_get_default. Should we pass through an application there, or change that to not track a default itself, but manage the default window in the application (like the other windows) instead?

If we manage it via the application and expose a purple_application_get_default_window that seems like it'd be more consistent than what we have now?

I assume you meant pidgin_application_..., not purple_application_..., but I actually wonder if we need to expose the default.
I did see that it's used in the Windows event loop, and it's to present the window when a message comes in from a second instance. But isn't that all handled for us by GtkApplication emitting the activate from a second instance? At least on Linux that's the intention, so I wonder if we need this at all on Windows. I'll go look at GTK, but then it wouldn't be necessary.

The only other thing I could think of where it might want to be exposed is a system tray, but that can just call an application action so yeah we shouldn't need to expose it.