Hi Adam,
To answer your initial questions...
The group you're clicking on your taskbar, is this a Saved Group?
No, I don't use "Saved Groups" at all. I have a few programs set to automatically group (FireFox, OneNote), then I have others which I do manually (Directory Opus).
Is the saved group pinned to your taskbar?
Again, I don't use "Saved Groups" and I also don't pin anything to my main taskbar. But please read-on for some important caveats related to this...
Does this match with your experience at all?
What you're showing in that video seems very buggy behaviour either way...so kind of glad it's not just me. But in regards to the specific question...
The second part of your video does resemble what I'm seeing...but maybe because my PC is relatively older or has more active programs running...the glitchiness seems a little more dramatic!
It'll appear, disappear, and attempt to resize the window from maximized to the most smallest size possible. Sometimes I even get a situation where the window finally appears at the forefront...but it's been resized to such an extent that only the close button shows.
If you're experiencing something different than this, I wonder if you could capture a video showing what's exactly what's happening (including the exact group formation steps leading up to the behavior, as I did in my video?)
OH! Important thing I just realized! This is something you can include in your test environment...
I use "RamMichael 7+ TaskBar Tweaker" (latest version 5.15.1). This allows me to organize my taskbar items in whatever order I want. The default Windows 10 taskbar has too many annoyances for me. So this is "critical" software - and not something I can abandon.
These are the settings I use (link to screenshot): https://ibb.co/jgVJGk1
While your video indicated the "Show only one combined button" is a little flawed in its current implementation...I wonder if there's also a conflict between Groupy and Taskbar Tweaker? Hopefully you guys can iron this out and workaround...because Taskbar Tweaker has no alternatives and isn't really updated much.
P.S.
I need to learn + install software related to desktop video recording. So give me a few days for that. I'll have video for you next Tuesday (very hectic for me these next three days with house chores, visiting family, etc.).