Chess games are rarely decided by one single factor. Pawn structure is important, but White can play Kh1 and Rg1 making their king safe at least in the short term.
Black's plan should probably be a slower one, trying to exploit the weak squares left on the enemy kingside. Perhaps that'd lead to a mating attack but it could also be just a favorable endgame.
...Nh5 is a decent way to start here as the knight can now think of jumping to f4 (probably the most exploitable weak square in White's side of the board) and it also threatens to trade the dark-squared bishops (that would make the f4 square even harder to protect). If White decides not to trade and retreats with their bishop, then Black can respond with ...Bd6 keeping control of the f4 square and preparing an immediate attack with ...Qh4.
The game could probably continue with something like 1...Nh5 2.Bxe7 Qxe7 3.Kh1 Qh4 4.Ne2, with Black starting to put pressure on the different White weaknesses.
But even if Black went just 1...0-0, their position would still be fantastic, as they're keeping a better pawn structure and more active pieces (for instance, what's the bishop on b3 supposed to be doing?). It doesn't look like White can really attack through the "g" file, as not many pieces can really join in. On the other hand, leaving the king in the middle could cause trouble later on with sacrifices on b5 or d5 to open up the position (also tricks like 1...Rc8 2.Rfe1 h6? 3.Bxf6 Bxf6 4.Bxd5)