Mouse lag/delay when switching to/from Blender (3D)

Since Blender v.4.0 (incl. updates), I have a delay for about 5 seconds, when I switch to and from Blender (revealing from hidden/hide on switch). Magic Mouse and another Dell mouse. Older versions of Blender is still fine.
I suspect BTT because when I tried with a clean user account, it was fine until I started BTT (though less lag than in my main account). However it doesn't go away just by quitting BTT.
I'm on MacOS Ventura 13.6.3