This is the question to the answer. You need to know it's inside circuit, not it's external circuit.
I assume with changing power supply there will be changing inside currents causing the phase or gain to change (open loop).
Power supply changes means bias conditions changes and hence you have different AC characteristic. There is no formula for this. The same is why AC characteristic changes across corners. From the same reasons. Different bias conditions.
If bias current has a supply dependence then so will
other attributes such as bandwidth and stability. A
solid quiet bias generator and distribution is key to
PSRR and consistency of frequency response.