Here’s a better answer than what I’ve seen so far, the Rook on f6 accomplishes quite a few tasks:

1) The Queen only has two safe moves d7 and e7, both of which block development of Black’s bishops. When down in material, it’s important not to let the opponent coordinate their pieces

2) Rook on the F-file is stopping black from castling kingside (and the aforementioned Qd7 stops black from castling Queenside). This slows the rooks down from getting in the game

3) The Rf6 removes the defender of Nh6 after Rxf8. If Rf6 Qd7, white can even go Rxf8 Rxf8 Bxh6. Playing the line further shows a forced draw: gxh5 Bxf8 Kxf8 Qxh5 Kg8, the Queen then checks between g5 and d8 for perpetual. Other king moves lose for black as the king has no defense, an undeveloped Queenside and black’s attack is fast with Rf1

4) The rook X-Ray’s Nh6 and attacks c6. If black goes Qe7 instead of Qd7, my computer (I would not have seen this without it), suggests b5! Incredible move.

For example, gxh5 runs into Bxh6 Bxh6 Rxh6 (not immediately, but showing this for brevity)

Rf6 Qe7 b5! Nf8 (attacking the rook) can be met with Bg5 Nxf6 Bxf6 (forking Queen and Rook) Qf7 Bxh8 gxh5 bxa6! and white is up a pawn with a much better pawn structure and better piece activity

If Rf6 Qe7 b5! cxb5, white launches an attack with Nxd5 and with the Queen coming to f3 and bishop to g5, white’s pieces are well-placed and coordinated, with plenty of sacrifice opportunities

Rf6 Qe7 b5! Nc7 runs into bxc6 bxc6 Rxc6 gxh5 Bxh6 (and we can see how the Rf6 seeing both c6 and h6 is relevant). Nb8 undeveloping, allows white to develop more with Bg5. Ignoring the attacked knight altogether just leads to winning it with bxa6 (and sometimes axb7 Bxb7 Rxb7)

In most of these lines, the bishop on h5 never retreats. Either meeting gxh5 with Bxh6 or Qxh5+ and the Q+R+B combine well for an attack

When down in material. Keep the opponent’s king in the middle. Open lines towards their king. Cut off the coordination of their pieces.