Thanks a lot for your awnser, it helped me fixing the issue!
I tried one by one each steps and nothing worked for me but the step 3 really stuck to my mind and I decided to change the whole cfg/custom folders and use someone else's.
The new folders made the overlay worked and when I switched back to my own files it was working perfectly aswell.
I really think there is a proper solution to find, imo it's about launching the game without any cfg/custom files to "reset" the overlay and what's causing issue with it, then putting back your files without changing a thing and it might works.
edit : I have been told (by zen) that if you have "-dxlevel X" set in your launch options it might cause that issue, also "mat_antialias" set to 1 could be responsible for that issue so try to set it to 0.