How Nimzowitsch Won

I MENTIONED yesterday how Tarrasch suffered the embarrassment of losing a drawish-looking opposite-coloured bishops ending to Nimzowitsch at Bad Kissingen, 1928.
The ending arose with Tarrasch to make his 38th move as Black (notes in italics translated from the German of those of an anonymous annotator in ChessBase's 2019 Mega database):

Black is a pawn down but has more space

The ending, which gives the impression of being clearly drawn, is won thanks to a hard-to-see subtlety of White's position.
38...Kb7 39.Kh2 c4?!
This may be a mistake. Tarrasch takes a pawn off the same-coloured square as White's bishop, but the pawn was not immediately vulnerable and now White's bishop gets more freedom-of-movement.
Stockfish10 likes 39...f4?!, which leaves Black two pawns down after 40.Bg5 e3 41.fxe3 fxe3 42.Bxe3. This looks very dubious as White will be able to create threats on two distant parts of the board - the classic formula for winning an opposite-coloured bishops ending.
Komodo9 prefers a waiting move such as 39...Bb5 or 39...Bf7.
It would seem natural to centralise the king with 39...Kc6, but Tarrasch must have seen something he did not like about it (or he just thought ...c4 was better). After 39...Kc6, the engines give 40.Kg3, and if 40...Kd7, then 41.Bg5, when Black can play 41...Ke6 with what seem to me to be reasonable drawing chances (a major problem with analysing endings like this is that engines tend to over-emphasise a material advantage as they have trouble seeing that opposite-coloured bishops will often in the long term neutralise such an advantage).
40.Kg3 Kc8?!
I am at a loss to understand why this would be preferred over 40...Kc6, although after Nimzowitsch's continuation in the game it does not matter whether Black chose ...Kc8 or ...Kc6.
41.Kf4
The engines reckon 41.Bg5 is slightly better (but that Bg5 would not have been after 40...Kc6).
41...Kd7 42.Bb4 Ke6 43.Bc3 Bd7 44.g3 b5
Tarrasch has moved all his pawns to light squares, where they are invulnerable to White's bishop, but his problems are not over.
45.Kg5

Black to make his 45th move

*****
*****
*****
*****
*****
45...Kf7
The engines suggest the incredible-looking defence 45...e3!?, the point being that after 46.fxe3 Bc6 47.Kh6! (this seems better than the engines' 47.Bd4), Black has 47...Be4, when 48.Kxh7? lands White in trouble after 48...f4+. However, given enough time, the engines come up with 48.Be1 Bxc2 49.Kxh7. This now looks strong as 49...f4+ is met by 50.Kh6 fxg3 51.Bxg3, when White has two passed pawns separated by more than one file, which usually gives good winning chances. Note that in each case ...fxe3, instead of ...fxg3, seems inferior. But also note that this whole line is complicated, so it is possible 45...e3!? really does give drawing chances.
46.h4 Bc8 47.Kh6 Kg8 48.b3 cxb3 49.cxb3 f4
49...Bd7 50.Bb2 A waiting move Be8 (50...Bc8 51.a4 bxa4 52.bxa4 Bd7 53.a5 Bc8 54.Ba1 A waiting move, and Black is in zugzwang) 51.Kg5 Bd7 52.Kf6 Kf8 53.Ba3+ White wins.
50.gxf4 Bd7 51.Kg5 Kf7 52.f5 Bc6 53.Kf4 Ke7 54.Ke5 Be8
Also hopeless is 54...Bb7 55.f6+ Kf7 56.Kd6 etc.
55.Kxe4 (1-0, 66 moves)