Who has the advantage in this position? I was in a three%day turn bame, I played almost played a line that would have led me to this position. Black’s central pawns seem to be an advantage, although White being up the exchange scared me. Who has the advantage in this position, and why?

It is White’s turn.
This position is not easy to assess. 

Indeed, white has a rook, but black has a bishop and two pawns for it, which is roughly equal material-wise.

Also there are no open files, so white's rook do not have a straightforward way to enter black's position. The best white could currently do is to try to create counterplay against the pawn on e6 and create a blockade on the dark squares, preventing black from advancing the pawns. Since black does not have a dark squared bishop that should be reasonably easy to achieve. 

As a long term plan, white can transfer his king to the queenside (e.g. to b2) and open some lines with g4, which does seem somewhat dangerous for black.

Still I think black is doing perfectly fine so far as the position is still closed, there are potential threats against g2 and the pawns are ready to run.

Overall I'd say the position is roughly equal (but interesting!).