How to DC bias the output of a Wien Bridge oscillator so that it oscillates about 2V?
Two things are happening in the circuit.

The actual centre voltage is the voltage at the GND of R1,R4. Connect them to 2V divider (bypassed by a C).

The second thing that is happening is the (exponentially growing) amplitude of the oscillations is clamped by D1D2. You need to adjust R5R8 so that this clamping is centred at 2V. If you were just clamping one side of the waveform, it would be introducing asymmetric distortion (i.e. having even harmonic content)