When from within Draw I click on “Help > LibreOffice Help” I am directed to a generic LibreOffice Help page at Help - LibreOffice Help
It does, but you need to press F1 or Help in a dialog box to get context sensitive help.
Help - [Program name] Help, or the top item in the Help menu of any program, will always lead you to the main page of the (inbuilt) Help system, often offering Help on how to use Help.
LibreOffice (as a whole) comes without offline help. There are specific additional installers for the offline help.
Did you install the offline help matching your version and (exactly) your UI language?
If so the offline help should be available for all the components of the software.