Bug 1860887 - Reorder JSON functions r=jandem

Follow the order in the header file, and group by class to make them easier to
find.

The exceptions are: I kept JSONSyntaxParseHandler near JSONFullParseHandler in
JSONParser.h because their interfaces need to be kept in sync. I kept the
JSONSyntaxParseHandler definitions in JSONParser.cpp near JSONSyntaxParser
because they need to work closely together.

Differential Revision: https://phabricator.services.mozilla.com/D198321