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Because if you play 1. Ng6+ first black will play Kh7. 2. Nxe7+ doesn't work because black can just play 2... Qxe4+

Yes you are right, but than I can play 2. Qxd5 and 3. Nxe7.

Yeah that's the main idea imo. I guess that's correct too :D

Yes, by the way I am not exactly sure if white win the bishop, cause after 1. Ng6+ Kh7, 2. Qxd5 cxd5, 3. Nxe7 black can play 3 ... Re8 cause the Knight have no square to move away, but 4. Rf7 protect the knight and the black king cannot move to the rook.
But IMO white can win easily with 5. Nxd5 exd5, 6. Txd7 and if black try to prevent this with 4. ... Rd8 white answer just something like 5. h3 and black need to move something but has no good move.