The gradual freezing out of the outer core to grow the inner core indirectly sustains the magnetic field generated within the outer core. (And even then "only" for the past ~0.5-1.5 billion out of 4.55 billion years of Earth's history, because the inner core didn't exist before then.)

However, the inner core itself doesn't really do anything practical or of non-academic interest. Aside from very slowly getting bigger, it just spins along (very, very slightly more or less rapidly) with the rest of Earth. The motions that power the dynamo are strictly within the molten portion of the core. Essentially, the combined motion due to Earth's rotation and core convection organize into rotating columns within the outer core, which sustain Earrh's intrinsic magnetic field. (See dynamo theory.)

The geodynamo is NOT because of the inner core rotating relative to the outer core, which it barely does. Because the inner core is a solid within a relativley low viscosity liquid, it can rotate at a slightly different rate. If anything, the electromagnetic forces associated with the dynamo act on the inner core in a way roughly analogous to an induction motor, exerting torque on the inner core and spinning it relative to the outer core. (The inner core never spins at a rate very different from the rest of Earth--inertia, conservation of angular momentum and energy, etc.) Even in this sense, which is not nearly as dramatic or impactful as clickbait would have one believe, the inner core is a passive component.

u/swirlyglasses1