Help on turning starlight in to voltage
I think that in order to maximize sensitivity you are going to need to use an amplifier. There are two basic modes of operation: photovoltaic mode and photoconductive mode.

In photovoltaic mode, when using a transimpedance amplifier, the voltage across the diode is held at zero volts, and the amplifier converts the diode output current to voltage. Zero light means zero current and zero voltage. There should be no dark current.

In photoconductive mode, the diode is reverse biased. This mode also uses a transimpedance amplifier to convert current to voltage. In this mode, a certain amount of reverse leakage current will be present, and thus must be calibrated out of the measurement.

Unless you can find a good reference, you may need to try both modes. Here is an image from thorlabs (my main source of information):



Note in the diagram that the basic connection is the same for the two modes. It is just a question of whether the anode is connected to GND or to a negative bias voltage.

I found the image here:
https://www.thorlabs.com/tutorials.cfm?tabID=31760