Need your endgame knowledge

I reached this endgame position as black in an OTB game. lichess.org/analysis/1R6/1P4k1/7p/8/6pP/1r4P1/6K1/8_w_-_ I think I can manage to draw but Stockfish says +3.3 but I can't see the win. How can white make progress here?

Just play it against stockfish. ;)

Ok, I looked deeper after h5 either way ist looks pretty drawish, some sort of a fortress. Compare the rooks, the active one compensates for the missing pawn.

The computer evaluation which remains high but equal (doesn't change) is a evidence for a fortress.

The evaluation drops to +0.34 or smth similar after some play, even if white takes pawn on g4.

Can't white just play Kf2, march the King to c2 and then to c7? Black can only play Kh7 - Kg7, as Kf7 leads to Rh8 threatening c8Q or Rh7+ and Kf6 or Kg6 lead to Rf8+ and Rg8+ followed by c8Q.

Where are you gonna go resp. gonna hide from the distance checks?

To #4, this was the first plan I had in mind for white, but the black rook can check the king infinitely and the king can't protect the pawn and hide himself at the same time.

The problem is that the white rook is in front of its pawn. The rook can't move without losing the pawn. But you can't make progress without your rook. So you need to give up the pawn if you still wanna try something. After losing your pawn to free your rook the material is equal and it's easy for black to draw. Maybe the winning chance was before when the pawn was still on c6 since the white king could hide behind the pawn on b7 but white would lose the g pawn and black could have strong counter attack based on the passed g pawn.

this is basic theory
with the passer on the 7th the white rook in front and the black rook behind the passed pawn its a draw even if white has an extra pawn on the g or h file, which is clearly the best scenario white can get here