Rook G7

pawn to g7

If the black king goes and captures my rook I can capture theirs an get a queen.

If the black king moves their rook to safety, I can move mine back too, saving it. The pawn and bishop are mutually protecting each other, so no need to worry about king capturing them. Don't know where to go from here.

If the black king decides to move his pawn up to f6 well... free rook I guess? I'll just capture his rook with my pawn at g7 and upgrade to queen, he will then be forced to capture her, leaving the black king at f8, his pawn at f6 and my two pieces safe. Though I'm not sure it is possible to do a check-mate with just your king, a rook and a bishop.

Without looking at any other comments, Rook to G7

Bishop to F6,

Black to move rook to IDGAF,

Rook to H8.

Dunno what to do if black takes pawn, tho.

Rg7+ kxh8 . Rh8+ kg8 . g7 kxh7 . g7xf8=Q is it correct?

KG4

Bf7

The only valid move for Black is to move their rook, at which point you can play Rh8#

Edit: wait nope I'm just dumb, the black pawn can take the white pawn

Pawn to f7. Rook takes pawn. Queen takes rook for checkmate.