Well it happened again! And it was indeed the shader compiler doing something funky. It was inflating the log with the same error messages till all hard disk space was consumed.
Failed to get socket connection from UnityShaderCompiler.exe shader compiler! (Filename: C:\buildslave\unity\build\Tools/UnityShaderCompiler/ShaderCompilerClient.cpp Line: 339)
When I turn my VPN off, this issue does not occur.
The other thing I discovered today was also interesting. It's related to URL protocols but I'll probably write about it tomorrow.