Models don't have any "climo" built in. The only aspect that would remotely affect it from a CC perspective is they have the atmospheric composition (how much CO2, etc) in there as constant, but this is updated every few years....so it's not going to cause any material affect on the model output on a 16 day solution. CO2 doesn't increase enough in a 16 day period to matter. Now, certain climate models that go out years might be affected, but usually those have built in emissions increases.
The laws of physics and thermodynamics do not all of the sudden cease to exist because of CC. So there is no magic "climate change variable" to switch on in an NWP model. The data from January 30, 2023 is going to get ingested in the models and they are going to run using equations that obey the laws of physics/thermodynamics/atmospheric dynamics.