Crushed by pawns - what happened?

I think your first 12 moves were completely fine. There may be more accurate moves, but none of your first 12 moves is a mistake. You start to go wrong with 13...Rc6. You try to attack c3, but white can defend it easily and 14.Ne5 is an obvious reply which gains a tempo. White can play c4 later to get rid of the weak pawn. 13...Bd6 would have been a logical follow-up of 12...Nb8. White can still play c4 and I think black has a slight advantage. A more accurate way to get in Bd6 would have been 10...Qd8 though.

In the game white can also play 15.c4. Black wins the exchange if dxc4 Nxc4. White consistently refuses to play Ne5 and c4 and as a result you can get a fine position after 22...Nbd7 23.Bg3 h6. I think you lost the game, because you did not see what your opponent could do. The position is also easier to play if you trade off white's annoying dark-square bishop.

You didn't try to counterattack. When you are facing pawn storms, it is important to counterattack in the center with a pawn break. You needed to move the Knight out of the way of the f-pawn, play f6 and then e5.

Pesky Pawns...

I would literally choose removing all my opponent's pawns over their queen and both rooks, that way I wouldn't lose in positions like this: