Electrical – Diagram symbol for an inductance with a neodymium magnet as a core

If the permanent magnet is a lump of iron then it is also a ferromagnetic core.

If it's magnetised so that it is saturated (off at one of the flat ends of the B-H curve) I'd expect its permeability to be lower than the unmagnetised core, and that will reduce its effect on the inductance.

Hmmm, that must be how those so-called "permeability tuners" worked - move a magnet closer to a ferrite coil, saturate the ferrite, tune your TV that way... Lossier (because of that part-saturated core) than a straight capacitance-tuned circuit but it used to be popular in cheap consumer electronics in the 1960s? 70s?

Someone was looking for an alternative to a voltage variable capacitance just yesterday... maybe this (control DC current and hence magnetisation in a separate winding on the same core) might answer his purpose?

If you are building a radio receiver probably it could be better to wind them separated on two pieces of insulating tubes in order to find the best position on the ferrite rod and the best distance between them. This because, depending from the circuit, the coupling coefficient and the inductance can be independently tuned. The 23 uH probably will load the 470 uh tuning coil and the loading is varied by distance. If you need some ferrite rods, i bought many about 30 years ago for another use.