a specific amount of energy (watts?)

Energy is measured in joules. Watts are joules per second, and a measure of how quickly the energy is being used.

And from there to absolute zero (0K) would be “available energy” in my perception.

No, it's not available. The only way to use heat energy is to find something that's colder, to be able to transfer that heat to, and use that heat transfer to drive some other process that puts the energy in another form: in a chemical bond, in an electrical charge, in a moving object, into moving something heavy higher, etc.

Once everything in the universe completely evens out in heat, where none of the heat can go into anywhere else (because everything else is just as hot), that's known as the heat death of the universe.

So if you're starting with stuff that's all the same temperature, and you want to make one part of that system colder by pumping heat out from the place to be cooled and dumping that heat into an already hot place, it'll always cost more energy than you can capture again when you try to use that heat for other stuff. That's because if you want to use that heat energy, the only way to do it would be to take advantage of the heat differential between the hot zone and the cold zone, by equalizing the temperature between two zones. Well, if you're going to do that, then why did you spend energy cooling the cold zone in the first place? It'll cost more energy to capture the heat as it returns to the cold zone than it cost to make the cold zone in the first place, so it would've been more efficient to just let the two zones remain equal temperature.