I think the main idea is that MOSFET chips don’t sink or source much current on their own (“fundamental” seeming to mean the way that current does not propagate into the gates, and most designs only really draw current during transitions)

OTOH some chips (amplifiers for example) may indeed have current flowing through them and therefore the power consumption of the “chip” would equal the sum of heat loss and output power. At least that’s my interpretation of the framing “how they operate at a fundamental level”. I could be wrong too, I’m not a working EE

It could go into the information directly. https://en.wikipedia.org/wiki/Landauer%27s_principle

LEDs are chips; some of the energy goes to light (which will be heat eventually, but not necessarily locally). Some chips also have measurable piezo effects, turning some energy into sound. And of course various data storage technologies (eg floating gate flash) have higher potential energy in one state than the other, so write operations may take more energy than is converted to heat.

The capacity of an object to radiate heat has essentially nothing to do with material properties. The equation is entirely dominated by surface area and nothing else. It is purely a matter of geometry. Which is why we use aluminum: it's cheaper and its lower thermal conductivity is pretty much irrelevant.

Not really. They use aluminum fins because they are way lighter and cheaper. The copper tubes are actually heat pipes that transfer the heat through liquid/vapor phase change. And copper is used because the liquid inside is water (aluminum would corrode) and they are also easier to bend into shape (aluminum fatigues easier with bends, and pores would allow the liquid to escape).