I believe I've nailed down exactly what's causing this after creating a new user.
I like having the "focus follows mouse" setting enabled, which can be accomplished like in this article: https://winaero.com/enable-xmouse-window-tracking-windows-10/. I have ActiveWndTrackTimeout set to 0. It seems to be a focus issue.
This is not an issue with Start11. I can confirm that I do also see the issue with the standard Windows 11 taskbar. (Presumably the behavior was different in Windows 10; I don't remember seeing this previously.)
I'm guessing I can work around this by setting ActiveWndTrackTimeout to a small non-zero value, but I'll give it a try when I have more time.