(note, this is NFHS rules not OBR)
From my "interpretation", an error is charged whenever a fielder's misplay prolongs an AB (9-5-5). Therefore, the fielder IS charged with an error. However, 9-3-2 which defines a base hit being credited only calls out: "A base hit is credited to a batter when the batter advances to first base safely: (a) because of the batter's fair hit (rather than because of a fielder's error)." For the pitcher, 9-6-3 would call it out as unearned because if you walk it back, the error would have retired the batter preventing the home run.
My reading of this would say that you score an error on the fielder (because not all errors require an advancement of a base like most people think), a hit/home run for the batter (the FAIR hit was not a fielder's error), and an unearned run for the pitcher.
I'll also add, there is ambiguity here that could allow you to justifiably score it the other way, but I will not. Scoring is 90% science and 10% art - and this is probably one of those "art" situations.