boot – Macbook turns off after a minute – not in safe mode, but in all modes of recovery

Problem

My friend's Macbook suddenly turns off on a black screen (as far as I know without a log) after booting. Take that. 1 minute.
The last thing he remembers doing differently is plugging in an external sound card (but it did not crash until the next day). Bearing this in mind, the audio does not work in safe mode and we do not see any internal audio device in normal mode.

The strange thing is: we can start in safe mode and everything works fine (except the sound). However, when you try to boot into recovery mode (on disk or online), it shuts down before the mode is fully loaded.

Tests / Diagnostics

the re Hardware test says that the material is fine.
In safe mode, we can run First Aid and complain "invalid btn_btree.keycount" and "fsroot tree is not valid – what it can not fix." We could probably fix this problem in mode Recovery (but can not enter it) or User mode (but it is Mojave, so it does not exist).

When you try to start in online recovery mode, it reproducibly reproduces: download everything, start to boot, then flash once in black, then display a beach ball, and then turn off.

Things we tried:

  • reset NVRAM, SMC
  • move all Kexts in extensions to the desktop
  • reconnect the external sound card

Then our questions are:

  • Can we somehow repair the recovery partition from safe mode? Is there another way to run Disk Util (target disk?)
  • Can we somehow erase the SSD, then restore from Time Machine?
  • Will creating a bootable USB drive help you? Is there any reason to hope that this does not just close (which seems likely to us since the Internet Recovery does)?
  • There is a new Mojave update that we could try to install in Safe Mode (but we suspect that it will not work / help)

And yes, the warranty is in place. The drive is encrypted and has a firmware password. It has a current reserve and no money, so we would rather use nuclear than take it (the problem is we do not know how – target disk mode?).