xps 13 9300 crash when using its main display

Hi

I have been using my dell laptop (xps 13 9360) without any main issue for the past 2 years. The update to windows 11 went smoothly, and I was quite happy with it.

However, for one week now, every time I'm using it with its screen opened, the display will go crazy after a short while, and it will crash. It's not a blue screen, but the system become completely unresponsive, and I need to force reboot it. However, I noticed that if it's plugged on a docking station, and I'm not using the Dell screen, I don't have any stability or display issue.

Hardware check didn't detect anything. I have done a factory reset of Windows 10, with latest drivers and MS update, so I could consider the laptop as completely vanilla, but the problem is still there. It either display a rain of pixel, or the screen is suddenly splitted into 2, with a black part on the bottom.

Any advice would be welcome.