Reasoning behind the Bg5 h6 ... g5!? lines in the Hyperaccelerated Dragon

In many lines of the Hyperaccelerated Dragon h6 is a solid response against Bg5, immediately chasing away White's dark-sqaured bishop and preventing a future Bh6 after the creation of the Queen-Bishop battery with Qd2.

If White retreats the bishop on h4 or f4 a weird situation arise: most of the time the move g5!? is the top stockfish recomandation, in the remaining cases g5 is a full error, not a simple imprecision.

I think it's more or less intuitive to understand why g5 can be an error since it weakens the king's defense, but I can't grasp why it is such a strong move when it is not an error.

The bishop often retreat on g3 adding another defender to the king and the lines suggested by stockfish looks totally crazy often pushing f5 an launching an all out pawn attack resulting in a completely exposed king.

As an example this is from my most recent rapid game (clearly the discussion is completely general and I would prefer not to talk only about this specific example)

Can someone with a better understanding of the Hyperaccelerated Dragon enlighten me?

When ...g5 wins a tempo then it is better than when it does not win a tempo.
In your example 12...g5 not only unpins Ne7 and frees Nc6 from defending Ne7, but after 13 Bg3 Bg4 14 Nbd2 f5 also threatens 15...f4