Hi @figmentPez . I do not remember disabling the ea overlay, but "luckily" that app bugged again and logged me out, so I had the perfect opportunity to double-check this solution.
So I went to the application settings (all of which were disabled by the way, even though I did not do that the last time I launched this bug nest) and made sure that the in-game overlay option is disabled.
I killed the application by exiting and ending the ea background process in the Task Manager and tried adding the ea desktop.exe to Steam as a non-Steam game.
After that I, again, verified that no ea processes were running in the background. I checked that the Steam Input is enabled for Mass Effect LE and then I launched the ea app via Steam, and shortly after that I launched ME LE, again via Steam (not ea app, as it was written in this method that I have found on the net).
Sadly even with the ea overlay being disabled - it did not fix the issue.
P.S. : The Steam overlay was enabled for ME LE during testing.