Audio related problem is crashing my Macbook Pro

My Macbook Pro started crashing out of nowhere. First it was infrequent (once a week). A month or two later and it wouldn't stay on for more than ~15s without crashing.

I've taken it to an official store for repair and after getting it back the problem returned a few months later. Nobody on Apple Support seems to understand the problem, so I thought I'd fish to see if anybody in the community has experienced this.

I'm convinced it's linked to the audio engine. Crashes absolutely never occur while Logic Pro X is open, or if I'm in a voice channel on Discord. As soon as these are closed, however, it's only a matter of seconds before the Macbook crashes (without fail). Crashes also occasionally occur while switching output/input devices on Logic Pro X.

Crashes go as follows: the screen turns to a black (but still backlit) screen, while the keyboard is still lit. After ~5s, the internal fans become audible and slowly creep up to full RPM over the course of ~10s. Then, the Macbook shuts off (signalled by the screen backlight, keyboard lights and fans all stopping at once).

Since official Apple Support have been repeatedly dumbfounded by this (and rightly so), I've just been living with it. Now, however, I want to update Logic Pro X to 10.5.1, which first requires macOS Mojave 10.14.6, itself requiring a restart for installation. Unfortunately, the Macbook crashes while installing on startup, presumably because it has no application open engaging the audio engine (this also means I'm unable to shut down the Macbook via the "Shut Down" menu option without a crash). I'm currently stuck on High Sierra 10.13.6.

I apologise for the lengthy post. All I want to do is update the OS so I can update Logic Pro X. If there is any way to do this without a restart, that would be enough of a solution.

Thank you in advance for any support that can be offered. Stay safe.