Then i will help for others :
I found what was not working was the cross pad (not sure how it's called in english, the four arrows that allow you to use tactic view and stealth mode). It get stuck and won't let you do anything in any menu.
Using big picture (on steam) and changing the settings of the controller, disabling any way to use those buttons, solved the issue. Though it means i have to use the hotbar to stealth and aim. A bit anoying, but far less than the original issue.
