A compost heap the size of the sun would not outshine the sun. The sun is plasma. And the energy density you quote surely doesn’t count the matter in that cubic meter, which at 20 million degrees kelvin, is rapidly turning into energy as well. That’s the problem with using energy density in a context in which energy and matter are not conserved.
Come to think of it, a compost heap the size of the sun would certainly collapse into a black hole, sucking the entire solar system in with it, so maybe I’d better not underestimate compost heaps...
Except that it isn't rapidly turning into energy, it is taking billions of years to do so, and even then over 99% of the mass is retained in the helium that is produced. That is why the energy density is so low. If it was much higher, the Sun would have baked the Earth and then run out of fuel long ago.
The low rate of energy production in the Sun illustrates the difficulty of fusion power - hydrogen compressed to a density of 150 g/mL at a temperature of 15 million K only generates ~275 W/m
3. Fusion on Earth requires a reaction with a much larger cross-section, the easiest being the deuterium + tritium reaction. Even then, the temperature needs to be 10-20 times higher to achieve a self-sustaining reaction.
As for a star-sized compost heap, the organic matter in compost consists primarily of hydrogen, oxygen and carbon. A late-stage red giant star has a fairly similar composition. Such a star the size of the Sun would be over a thousand times brighter than the Sun (due to a hotter, denser fusing region with a much higher energy production rate), and would be evolving quickly towards the white dwarf stage. No black hole would be formed, that would require more than twice the mass of the Sun.