Does op-amp open loop gain change with DC input voltages versus small-signal AC input
Let's first get this out of the way: the inputs have to be very close to each other in voltage for the op-amp to do anything besides be a comparator. This is because op-amp open loop DC gain is large, in the thousands to tens of thousands, and can vary by an order of magnitude in some cases. More about that here: https://www.analog.com/media/ru/training-seminars/tutorials/MT-044.pdf
That said, an op-amp can be configured with feedback to amplify DC as well as AC, small signals or large. It will nearly perfectly give the gain you're seeking so long as you understand the limits of what the particular op-amp you're using can do.
I think maybe what you're asking is, &quot;is the gain affected by the DC offset of the signal pair?&quot; The answer is yes, somewhat. The specification for this is expressed as the Common Mode Rejection Ratio, or CMRR. More about that here: https://www.elprocus.com/common-mode-rejection-ratio-cmrr-operational-amplifier/
Op-amps also have input offset error which affects DC gain fidelity.