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34... Ne6 seems to win a pawn due to threath Nf4+ (35. g3 Ng5).
In general, the ending should be good to black because his pawn majority on the kingside is dangerous whereas white's pawn majority on the queenside is compromised because of the doubled pawns. Black should possibly keep the minor pieces with 35... Nf7.
I'm far from sure about this, but in the final position white might still perhaps try transforming the king to g3 and playing h4.
Good first Otb game! :)