Like in the original question - I'm struggling to understand the relationship between the op-amp on the right to the op-amp on the left. As far as I know, a Wein Bridge network is being used here but otherwise, I'm stumped.
The opamp on the right is just a voltage follower, and provides a low-impedance source to drive the bandpass filter (actually only half of a Wien bridge).
The opamp on the left is a simple inverting amplifier. VR02a picks off some amount of input signal (either in-phase or inverted) to feed to the filter. Since the source impedance at the wiper varies with position, the other opamp is used as a buffer so that this does not affect the bandpass filter response.
The output of the bandpass filter is then summed with the original signal to produce the midrange boost or cut.