What exactly do you mean by hooking into the UI system? There is no one UI system, and they are all interconnected in some ways but completely disjoint in others. The tips in general, again is overly broad - tips in general, I would say is best covered as: MSDN is a fantastic resource for documentation on the various subsystems that are involved here.
I think that this is what you might really be after. There is no current equivalent to any of that. There is no UI designer, the UIs are built programmatically. I was looking at the XAML hosting APIs for WinUI integration from Project Reunion. However, I ended up not going too far down that route as I kept running into issues with WinUI and I could not find the implementation for the hosting container (most likely because it isn't open sourced).
I would recommend that you read through the initializer for the
Calculator class to see how the controls are added to the Window, and the member variables for how the controls are actually created.