Great to hear, it sounds like you've already thought of a lot of these things! I'm loving Groupy so much that I keep seeing little things that could make it better/smoother and feel "right" with Windows. Feel free to ignore if unpossible, but without further ado, here are some more ideas
It's not about the focus but the focus rectangle. You're the low level windows expert, so I don't know if it's possible to make it look like it's focused when it's not (blue rectangle instead of grey), but it seems like it should be. You're already drawing the blue "app focus" highlight around the contained window when dragging over it, why not do that when the three seashells menu is open? Guess that could wreck the app if it was doing custom draw or something, but can you detect that with a window style?
Also, why not retain the blue highlight on the GroupyCtrl window when focused? I think that's focus hopping around makes it feel more disjointed than the contained window.
The no focus view looks great: https://i.imgur.com/mMbVoGQ.png
But then you focus and the outline around GroupyCtrl disappears instead of going blue: https://i.imgur.com/btmfRtX.png ... except if the left most tab is focused and then you get blue on the left, nothing on the top: https://i.imgur.com/kPrakmN.png
If dragging, you can get a hybrid of that where some tabs have the not focused line on the top but no left line and some tabs have the focused line on the left but no top line: https://i.imgur.com/HfeFyYV.png
And finally you open three seashells and the outline around GroupyCtrl goes back to grey: https://i.imgur.com/aCwwDeg.png
Just making Groupy's focus outline consistently there instead of disappearing sometimes, and blue focus when the menu is open seems like it would be something totally under your control and increase the feel a good deal even if you can't draw on other windows.
I didn't notice it until just now, but the background dropshadow behind the app only goes up to the app window and not behind Groupy.
Another unrelated bug I just hit: if you drag a window off a group and then back on without dropping inbetween, it still makes a new group: https://imgur.com/a/Sl6PC instead of dropping into the group it said it was going to drop in to. There's also an associated display bug -- after it fails to drop back into the group, if you try to drop it in again it flubs the tab drop rendering: https://i.imgur.com/TVavIRJ.png -- drop works the second time though.
Edit: on the topic of dragging, you should be able to hit ESC and cancel a drag in process. Even normal windows can do that.