Sorry but your analysis
@doom12384 is incorrect. Qf3 isn't mate, it's just a completely free queen.
After Qxd3, we have Rg4+ Kf1, Qf3+ Rf2, Qxf2#. After Rxd3, we have Rg4+ Kf1, Qf3+ Qf2, Qxf2#.
The queen can move off the second rank with Qd1 (ready to sacrifice if Rg4+), but then we have e2!! opening up the diagonal towards white's king, and the bishop will come to d4 in many lines. It's a forced mate in 4.
I agree that Queen anywhere on the 2nd rank leads to exd2. This is good because you're up a rook, but more importantly, you also have Bd4+ coming in pretty much every variation, so it's another forced mate (in 5 according to SF).