You are missing a tactic I believe. Bg2 is the winning move. It forks the knight and rook. I believe best response for white is to play Kf2 and allowing the bishop for a rook trade. Any other move loses the knight or rook for nothing I believe.
Help to understand why position is winning for Black

I guess I should have been explicit and said Black has the threat of Bg2, which can easily be defended as far as I can tell.

Thanks. Any advice on how I should use the bishop pair in this position? Where are they best placed? What pawn breaks should I be going for?
@6
The plan to win with an extra pawn is to create a passed pawn and queen it. In this case ...f5 and ...e4.
The most valuable bishop is the unopposed one: Bf8. This should be activated ...Bg7. Then the rooks should be centralised Rf8 and Re8 to prepare ...f5 and ...e4. The king can go to d7 or can castle O-O-O.

The position is better for black because the pieces have more attacks. If you consider the following:
Ne6, Bd5 Nxf2

Here is a position from the game, which is similar to the one I posted, evaluated similarly by the engine (-2.6). It is a little earlier on in the variation.
Black to move:
The queens will get traded and we will reach a position similar to what I posted.
Here is the position immediately before White offered a queen trade.
White to move:
This is evaluated at about (0.5), edge for White.
Is it the case that the queens neutralise the other advantages black has? How does a human think about this?
@11
"Is it the case that the queens neutralise the other advantages black has?"
++ Yes. With queens it is harder to convert the pawn and/or the bishop's pair.
With queens on the board Kd7 is insecure.
"How does a human think about this?"
++ If you are ahead in material, then trade pieces, not pawns.
If you are behind in material, then trade pawns, not pieces.
Helllo!
I am ~1200. I recently played a 3|2 game with Black
https://www.chess.com/analysis/game/live/63169153847?tab=analysis
(The game itself is not that important, but may provide some context.)
After analysing with the engine later, I found a variation which I did not go into because I did not realise how good it is for Black (-2.4). It's White to move here:
My question is, how do you evaluate this position?
Black is a pawn up, which at my level is about is a slight advantage. I do not see any immediate threats Black is making. The extra pawn is a hanging pawn; Black has the bishop pair.
Can you clearly see that this is almost winning for Black? Is it obvious? Are there positional features here I should be looking for?