I think that this is a very interesting game worth studying.
The ending is a draw as stated, but I think that if the pawns are on f4 and f5 instead of g4 and g5, then it is a win for White. (After putting the pawn on a7 and the rook on a8 then the Black King can't go to f7 because Rh8! wins for White, because after Rxa7 White has Rh7+.) So White eventually wins the f5 pawn with his King, and then White marches the f pawn up to f6 throwing the Black King off his g7 and h7 defensive squares. I just confirmed this with endgame tablebases.
What I have a hard time wrapping my head around, is why doesn't this same strategy work with a G pawn? The answer is that Black can set his king on g7 and give checks with the rook. With an F pawn then the Black King either ends up on f7 which loses to Rh8, or it ends up h7 allowing White to play f7 threatening to queen.
However, I am just assuming that the Black King just goes between g7 and h7. There are other possibilities, but these are winning for White as well. https://syzygy-tables.info/?fen=8/6k1/R7/P4p2/5P2/r7/6K1/8_w_-_-_0_1