There were some great articles on it, in a survey by New in Chess Yearbook.
It was an update from a previous work by GM Wahls.
U can find it here :
https://www.newinchess.com/KG_Declined-so-152.html
I've just noticed there was another update, so u have the choice between both (108 and 114).
Of course u will have to pay, but it worth it.
About 4.d3, it is rather dull (compared to exf5), going into kind of king's gambit refused where white and black can't play Bc4-Bc5, and a symmetrical position...
One example where the better player takes the point :
does anyone have an idea what theory says after 1. e4 e5 2. f4 Nc6 3. Nf3 f5 4. d3 I couldn't find any good ideas myself, although this seems the move im facing the most.