After upgrading to 3.0.6 it seems I cannot replicate behavior I had before (even by downgrading StartAllBack) but let me explain it, this is how it worked on my system.
In unmodified system holding (not tapping) "Alt+Shift" or "Win+Space" would bring a Language Switcher flyout/popup like this:
Prior to version 3.0.6 of StartAllBack if I would set "Corner icon open:" to "Windows 10 flyouts if possible" then Language Switcher popup would not appear from holding "Alt+Shift" at all. Even clicking on Input indicator on taskbar would not show anything else. It may have been a bug but this is what I want to have.
After upgrading to version 3.0.6 option "Windows 10 flyouts if possible" now makes it so Language Switcher flyout/popup shows up as it intended by changelog:
Now, the behavior I wanted to see is the one I had before upgrading where Language Switcher popup did not appear at all, if such thing is possible.
Currently one of the ways to disable Language Switcher popup is to disable Action Center altogether which also disables all notifications and that is rather big side effect to have.