A Crazy Position for my Human Brain. Is White even Losing?

This is from a puzzle. The reason I am posting it here is because I think there are so many interesting possible and counterintuitive lines besides the precise solution. Black is up a queen, a knight, and two pawns on material. It's white to play. Since I saw this in a puzzle, I figured there was a way to force a draw. In a game, I would have assumed that Black could have forced a win and would have probably played differently. This is the sequence of moves I initially thought of when I saw this puzzle:

I'm thinking the Black might take the bishop, allowing me to force a draw by threefold repetition.

However, Stockfish initially says it's a draw, but it recommends an extremely different move to secure the draw, but it then says it isn't even a draw but a win for White. This leads to a mate by 7 moves:

Black should be fighting if he goes Rg1 Ne8 Rg4 Qd8 Rh4 Qxf6 exf6 Nxf6 and there is no mate

سلام