Measure the output voltage of photodiode in parallel with a laser diode
To measure the photodiode response, you need to disconnect one end of the photodiode or the other from the laser. Typically, laser diodes packaged with monitor diodes are connected either "common cathode" or "common anode" (although other arrangements are possible), meaning the two cathodes or two anodes are connected to one pin, but the other two pins are separate.

With the arrangement you show, any photodiode current will just be a tiny offset to the amount the source has to supply to the laser, so it will be very difficult to measure accurately. Furthermore, the photodiode voltage will not be meaningful because it will not be able to supply enough current to change the voltage across the laser significantly.