I forget who told me about it but essentially I went through the same process as you and learned of it on these forums.
To the best of my knowledge ScriptContext is not really it’s own “section” of the API, it’s a wrapper for RhinoCommon so you set the script context to the rhino doc and then can access the full RhinoCommon methods and such and vice versa when the scriptcontext is set to ghdoc.
If I’m wrong on that, hopefully someone corrects me. I’m new to Python and Rhino scripting in general, learning as I go.
I don’t know much more information about it other than what’s in these links:
The .pdfs in this post are helpful as well though not directly covering ScriptContext:
I think it was summed up fairly well (based on my limited understanding) in the first forum post I linked, that it’s like a bridge between the Grasshopper Doc and the Rhino Doc which are two, independent documents.