kicadian – I suspect you are on the right track already, but let me comment that one of the most important Kicad topics to get clear on is how Kicad (schematic and pcb) finds libraries. As with many software packages (such as programming language build systems and IDEs), this is accomplished with “paths” of some kind, so the key piece of the puzzle is understanding where these paths are stored (environment variables, initialization files, project settings, user preferences or whatever).
For Kicad, it’s not rocket science – just paths pointing to where libraries are. But it’s maybe not the most prominently presented information, and the complete picture is not necessarily visible at a glance.
The doc you pointed to for Kicad 5: Library management in KiCad version 5 … goes a long way to describing that for Kicad 5.x, and I absolutely would not want that to disappear any time soon. It is marked for Kicad 5, and hopefully a Kicad 6 version with appear (or maybe exists already).
The flip side of this is establishing, based on the available path mechanisms, your own regimen of directory and file locations for your own “all projects” libraries and “per project” libraries.
This is fundamental to feeling in-control with Kicad.
You may also be interested in a thread of mine that relates to this topic, and particularly the role of kicad_common (kicad_common.json in K6): Kicad_common 5.x 6.x details please? - #2 by qu1ck
As a side note, your questions about github may relate to a previous experience with earlier version Kicad where I believe the Kicad application itself knew how to visit github and fetch library updates. That is, github was being used to distribute updates for the kicad libraries ad hoc, rather than library (official) updates only happening through updating the application. I’m not sure what happened to that functionality, but whatever the convenience was, it left some sense of not being entirely in control of what libraries Kicad could actually be expected to use.