MacBook Pro (M1, 2020) won't boot - shuts down after fan noise

When booting my Macbook pro, the Apple logo and progress bar appears, it makes some progress, but then the fan starts spinning and after 2 seconds or so the computer shuts down completely. Trying to boot into Safe mode or Recovery is impossible, as the same exact thing happens! Connecting a power supply makes no difference.

What puzzles me is that I was in the same situation a week ago or so. That time I opened up the Macbook to see if anything abnormal was visible (there wasn't.) But for some strange reason, after putting back the back cover, the computer started as normal!

I immediately ran Apple Diagnostics, but no problem was found. So I went ahead and used the computer as normal. Everything seemed fine except that the fan started spinning at high speed at random times, even without any CPU/GPU-heavy app running. I installed iStat menus to check the temperature sensors but everything looked OK (25-35°C.) Today the aforementioned problem returned: boot - fan noise - shutdown.

Is my Macbook giving up on me after only 2 years? 😢

Model: MacBook Pro (13-inch, M1, 2020)

OS: Ventura 13.6