Opposite Exceptions (part four)

Black has just captured on d5 in Vitali Braun (2224) - Spanton (2039), Hastings Challengers' 2001-2. How big is White's advantage?

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White has a slight edge, according to Stockfish12; the upper hand, according to Komodo 11.01.

35.a3 Ke6 36.Ke3 f6

From my original notes I see Fritz5 preferred 36...f5?!, but giving White an entry square at g5 is almost certainly wrong.

37.Bf8 Bc6 38.Kf4 d5 39.g4

The engines agree White has the upper hand, but Black seems to have a defence.

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39...Kf7?

Correct is 39...Be8, when I do not see how White makes progress.

40.Bd6?

This gives Black time to set up the best defence, so White needs to play 40.Bc5, the difference being the bishop is protected on c5. Then 40...Be8 41.g5 (this seems stronger than 41.gxh5?!, although Komodo11.01 disagrees) Ke6 42.gxf6 Kxf6 43.Bb6 Bg6 44.Bd8+ Ke6 45.Kg5 Bd3 46.Kg5 appears to be winning. The engines give best-play as something like (there are a lot of alternatives along the way) 45...Bc2!? 46.Kxh5 Kf5 47.Kh6 Bd1 48.f4 Kxf4 49.Kg6 Bc2+ 50.Kg7 Bd1 51.Kf6 Ke3 52.Ke5 Bf3 53.Bb6 (53.h5?! Bxh5 54.Kxd5 Kf4 is a dead-draw, according to Stockfish12, although Komodo11.01 gives White the upper hand) Kd3 54.Kd6 Kc3 55.Bc5 Kb3 56.Kc7 Kxa3 57.Kb7 Kb3 58.Kxa6 Be2 59.Kb6 Kc3 60.Kc6 Kc4 61.Kd6 Bf3 62.Ke5 etc. This is a very long line but I think it illustrates the winning method.

40...hxg4?

Ensuring defeat. After 40...Ke6 41.Bc5 Black has 41...Be8, getting back to the correct defence, eg 42.Bb6 Bg6 43.Bd8 Be8 44.g5 f5 45.g6!? Bxg6 46.Kg5 Be8, when White cannot make progress. White can try 41.gxh5!? but 41...Be8 42.h6 Bg6 43.Bc7 Bh7 seems to hold.

41.fxg4 Bd7 42.h5 Kg7 43.Be7 Bc8 44.Be8 Kh6?!

This cannot be right, but Black is lost anyway, eg 44...Bd7 45.g5 fxg5+ 46.Kxg5 Bh3 47.h6+ Kh7 48.Bf6 Bd7 49.Be5 Bh3 50.Bf4 Bc8 51.Kf6 Bh3 52.Ke7 etc.

45.Bxf6 Be6 46.Kg3 1-0