This time I caught it rebooting on its own during the day after a blue screen of death too fast for me to see the error code. I went to the Windows Event Log and I saw an error logged after the reboot but nothing specific at the time of the crash itself. It generated a dump I can't open by myself, which is a poor hint at what might be the problem.
The laptop seller offered me to repair the computer at their facility, but for that I first need to save my data on an external storage as I last transferred my data directly from my old computer to the new. I know I had some 2.5" drives stashed somewhere in my house so I ordered an enclosure.
However, I'm not able to find the drives anymore so I'll have to order an actual drive since I now have an empty enclosure, which will delay the troubleshooting process further.
Stay tuned for the next episode of my modern computer woes!