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White cannot force a win. However, if it manages to move the king to D7, and the black bishops leave the B8-H2 diagonal (a huge blunder), then white can move its pawn to C7, and checkmate in the next move, by crowning the pawn into a queen.
But while a chess engine apparently can't see the draw as long as there is a possible helpmate on the board, it can see the danger of leaving the diagonal so will never play this.
It's actually a shame, they failed to remove the obvious hint for this, which is the green x drawn on the hand drawn version of the puzzle.
Why not?

Once you're on D7 the pawn can be captured or kept. If black moves to capture the pawn with a bishop, you move the king into pawn's old spot. You capture the black rook with the other pawn for the win.

If there are no more bishops on the diagonal, or if they move their king to the B column, then you get a Queen and finish them off.

Am I missing something (I'm a very bad player)?

> If black moves to capture the pawn with a bishop, you move the king into pawn's old spot. You capture the black rook with the other pawn for the win.

If you capture the black rook, black will capture your pawn with the queen (and proceed to mate you now that their queen can move).

Why would it need to move the king? As long as the bishops move, moving the pawn and turning into queen or bishop wins.
Once the pawn moves to C7, black's king can play to B7. If white's king were not defending, black would be able to capture the promoted pawn in the next move.
They say black has to make a mistake for it to happen. So I'm guessing white promotes its pawn to a queen, after moving the king to a position where it can defend the new queen.

The mistake black makes is trying to get its king out of the morass as soon as the pawn moves, instead of just capturing the pawn with its bishops.