Here is an update.
I upgraded to patch 1.0.31+ but it did not fix the issue.
However, the post of MasterFighterr Game crashes when loading into Mourningstar with High Textures gave me the idea that maybe it was a high quality texture settings issue. But, unfortunately, it’s not possible to change the video settings before loading the Mourningstar (or maybe I’m wrong?). So I dug a little bit and found that settings are saved in a configuration file in the following path:
~/.local/share/Steam/steamapps/compatdata/1361210/pfx/drive_c/users/steamuser/AppData/Roaming/Fatshark/Darktide/user_settings.config
So I made a copy of that file and then deleted it to reset all my settings.
That solved the issue. I can now play the game again.
I have not fiddled with the settings to figure out which one is problematic with the new 1.0.31 patch. But based on MasterFighterr findings, I suspect it is related to textures.
I hope this helps.