Not finding the engine's best move is completely fine. But what I found changed the evaluation from +1.5 to -0.2. How could I think so that I at least sustain the advantage?
You only have "the advantage" because the engine found a complicated way to win.
This is not a type of position where white is winning no matter what. After a random normal move, white is only slightly better, due to the control of the only open file.
Your Qd5 move is worse than a random normal move because you lose your only advantage, the d-file. Black can play Rd8, forcing trades, and the resulting rook endgame is slightly better for black: black's rook is more active, and black's kingside pawn majority can is better that your queenside pawn majority where the b3 pawn is weak and backwards.
A good player would see Qd5 Rd8, and would play something else. A very good player would spot the Qe3 - Rd5 - Rbd1 idea and play that.
Not finding the engine's best move is completely fine. But what I found changed the evaluation from +1.5 to -0.2. How could I think so that I at least sustain the advantage?