Yes I found several topics on the MI forums, but the problems seem to differ from one persone to the other (some talk about a general noise, others about a high freq like mine).
I updated my post above with a picture of the spectrum of my background noise (I thought I had attached it before but I'm not sure if it was successfully embed from Dropbox).
The safest solution might be going back to LCD, it's a pity because it looks great and, who knows, maybe it's my precise OLED that is acting in this way and an other one would not… On the MI forum, most people who had issues or who are more sensitive to those issues on the MI forums went with this solution.
The thing I'm completely sure now is that it's mainly a proximity thing: I breadboarded the screen outside of the PCB and the issue is almost 100% gone.