I'm surprised at your rating you're playing 10...dxe5. 10...Nxe5 is the logical move. It's not played when e.g. Nc5 pressures e4, but here that's not the case, so of course you trade the comparatively passive and cramping knight for white's active knight.
Maybe it's just my QGD experience but after that a setup with 12...Qe7 and 13...Bb7 is fine. The bishop might look terrible, but white's bishop isn't going to get you on the a2-g8 diagonal for example, and it indirectly eyes e4. You noticed Qc7 is wrong in your notes (predictably the d and c files will be open for the rooks).
All this to say... symmetrical pawn structure emphasizes piece placement. Even if the pawns are the same, if your pieces are different then you can pressure your opponent. One player puts one of their knights to the 2nd rank for example, or one player gets their "bad" bishop outside the pawn chair first. Gains control of a center square and posts a minor piece there first. Those are some situations that come to mind.
In this game it didn't really get to that point because you made some poor general choices that had nothing to do with the symmetrical pawns structure. That's my analysis FWIW.
As for your question about books, I don't know any that deal specifically with symmetrical structures, sorry.
Does anyone know of any good quality books on playing positions with symmetrical pawn structures (for example, see diagram)? I feel that this is the area in which I am consistently outplayed (probably because the positions don't come up much in my opening repertoire).
In the game I get a Knight on a good outpost and my Rook on an open file and even to the seventh rank and yet lose by move 25.