I've read(†) that in AC circuits an ideal transformer with unloaded secondary draws no current in the primary. This is strange, because that's not the case with an ideal inductor (it draws current, though the power consumption is zero). An ideal transformer with unloaded secondary looks like an ideal inductor to me. The secondary has a voltage, but no current, so it doesn't affect the magnetic field and flux.
† Ask any AI chatbot, for example.