I know we are eliminating "Through the green" from the definitions, but doesn't the new Local Rule now necessitate a specific definition for "Fairway?"
Yes, and oddly, they don't define it in the released 2019 Rules. It's noted as a part of the "General Area" in 2.2 "Defined Areas of the Course" and in two other places: in 16.3 about the embedded ball, and in the definition of Advice regarding the "location" of the stated items.
Kind of odd that it's used three times but not defined. I mean, even "the hole" is defined, as is "animal" and other basic words that "everyone understands." It isn't defined in the current rules, either, despite the embedded ball rule using it.