But the move that Stockfish picks has been searched to depth 30 or even 50, depending on how easy or hard the position is. Its infeasible to actually search all possibilities, but Stockfish basically is searching "deep", to ensure that most obvious tactical patterns are accounted for (orderings of captures and stuff of that nature)

That's roughly the "shape" of Stockfish's search tree. Super deep for the moves it picks, but very shallow on its exhaustive search.