It’s definitely a driver thing. I realized I used the old Wacom driver 6.3.25-5. As Windows didn’t propose me another driver when I tried to update, I assumed it was up-to-date.
So I went to the Wacom driver webpage and saw 6.3.27-2 was the last one. I installed it, and now the mouse pointer disappears way less than before, and like @Nabuco if I press alt+tab 2-3 times everything works again.