“The minimum state of charge is typically set to 30-50% in order to avoid damaging the battery bank by excessive discharge.”  Is this the same as the setpoint state of charge set in the System Control Inputs?

No, the minimum state of charge and the setpoint state of charge are not the same thing.  The minimum state of charge is a property of the battery, which you can see if you click the Details button that appears in the Battery Inputs window.  You specify that number only when you create a new battery.  HOMER will never discharge the battery beyond the minimum state of charge, under any circumstances.

The setpoint state of charge is a control parameter that affects how the system charges the battery bank.  It is the state of charge to which the generator(s) will charge the battery bank once they start charging it under the cycle charging dispatch strategy.