My V-belt is screwed, and half the variator too?

Hello, first comes the facts, the real question comes in the last paragraph😁

Hello, I have a Peugeot Speedfight 4 4-stroke Darkside. I had it derestricted about two months ago (25->50), and it was already having problems back then. Regardless of that, something happened in the last few weeks. At first, it only went 30, then, as if by a miracle, it went back to 50.

Today, something happened while I was driving. Suddenly, there was a cracking noise, and it accelerated poorly, with high revs and little power. Since it was on my way home, I stopped at the garage. The mechanic listened to it (the variator was making strange noises) and told me what it could be. It might be a broken clutch. He said it would be best if I fixed it myself, as it's easy and doesn't take long. Then I went home, and 10 meters from my parking space, I found that the car was in neutral.
Engine turns, no power to the wheels.

First of all, the background.

Now I've opened the Vario, pulled out the torn belt, and want to unscrew [the part shown in the picture]. But it doesn't work; the screw keeps turning. Normally, I think you hold the part in place and then turn it, but now it's loose and won't work anymore. What should I do? Or rather, how do I get this screw off?

And can I leave it open overnight? Or is it best to close it again?