I think there might be confusion between "self sustaining" (a perpetual motion machine) and "self exciting" (using its magnetic field to convert mechanical power into electrical power to produce its magnetic field).

The former is not claimed. Earth's core converts mechanical energy in the form of convection currents into electrical currents and a magnetic field. When the core freezes solid, the convection will stop and the dynamo will end. Joule heating likely returns some of the energy to the inner core as heat, but that would still only prolong the lifetime of the dynamo, it would not sustain it indefinitely.

The latter is not in doubt, self exciting dynamos are used in large generators because permanent magnets have limited strength, and under the conditions that exist in the generators, very limited lifetime. Self excitation also been demonstrated in conductive fluid flows. They do not violate any laws of thermodynamics, the excitation current consumes some small percentage of the total mechanical power driving the system. Without that mechanical power, the field will quickly die away, but with it, a small initial field will be amplified up to a saturation point. In large generators, a battery or small generator (itself using permanent magnets or battery-driven field coils) is used to provide the initial magnetic field. In a star or planetary core, there's friction, thermal and electrochemical effects that are all capable of separating charges and creating the needed starting field.