Why does it take stockfish depth 35 to find mate in 7? - Chess Stack Exchange

My underlying question here is: What is depth? I know depth is supposedly the number of half-moves or plies from the starting position that it has calculated, in at least one line. But I feel this

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Had this position today! White to move. Stockfish shows +99 at depth=49, but can't find mate. How do you win as white? : r/chess

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