Does this harmonic balancer / crankshaft pulley look damaged?

Yes, that's the rubber damper developing a crack on the crank pulley. It will need to be replaced.

As the name suggests, the primary purpose of the harmonic damper is to help counter torsional vibrations and resonance. A non-functional damper results in excessive wear and tear on the crankshaft bearings as there will be nothing to dissipate the energy generated by the engine's harmonics.

If this crack grows large enough, the outer part will be effectively free to spin independently of the crankshaft. Once this happens, all kinds of weird symptoms can crop up.

Here is my own experience.