Mouse input blocked by transparent window when any msys shell is opened

I'm on Windows 11 and mainly use msys2 shells (UCRT64 mainly) inside MS Terminal, which means I run this command:

C:/msys64/msys2_shell.cmd -full-path -defterm -no-start -here -ucrt64

This causes no problem. But when I run msys2 shells in mintty, so the command above without -defterm arg, there seems to spawn a transparent window always on top hogging a region of the screen and blocking all mouse input inside that region. I am sure this is related to msys2 shells run in mintty because when I close the msys2 shell in mintty, the mouse inputs/clicks aren't blocked by a transparent window, and it's not caused by the shells in MS Terminal with -defterm arg, so something else is going on here.

Also, I wanted to run msys2 shells in mintty so I could use msys's tmux (it doesn't open on MS Terminal). When I spawn a tmux session, even if I then kill the mintty shell, the transparent window persists, which means it's not a mintty issue, either. From here, I don't know how to debug.

Start by reproducing the issue with the provided msys2_shell.cmd command, comparing mintty with MS Terminal and testing the behavior after starting tmux. Investigate which process owns the persistent transparent window; done means mintty and tmux sessions no longer leave a screen region that blocks mouse input.