> Despite its intense temperature, the peak power generating density of the core overall is similar to an active compost heap...
I've seen this comparison before and it also seemed quite surprising to me. But in hindsight maybe it shouldn't: The sun is already billions of years old and it hasn't burned out yet.
Another way to think of it: A larger compost pile has to radiate more heat out of the same surface area as a smaller heap because of the Square–cube law [1]. Now imagine a compost heap more than 800,000 miles in diameter.