If they can build a sphere or swarm megastructure then obviously they would have build orbiting habitats either from scratch or terraforming planets or astroids.

> The whole energy of the swarm will be used there

that sounds like a made up problem. the Dyson swarm isn't to collect energy to send to the home planet. it's to collect energy. where that is used is going to be wherever it's needed. mining the asteroids, local computing (the cloud is no longer just a computer on earth, it's the cloud of the swarm elements), powering interstellar trips remotely, etc. the only thing that needs to get to earth is the imports of goods and services.

Terraforming a planet is another use case.

Why would you use the energy on a planet? Clearly you would use the energy in space, probably in some of the same satellites that are gathering energy

There's Mathrioshka Brain https://en.m.wikipedia.org/wiki/Matrioshka_brain which uses the energy then and there for computation.

That actually makes no sense. You can't use (destroy) energy, you can only run it through processor, which will change it into heat while transistors inside are switching on/off. It is like a water wheel doing work by water flowing through it, but ultimately amount of water before and behind water wheel is same.

Thus the question still stands, what happens to heat in such thing? Does it get recycled by some unknown device? Then it is closed system, you don't need input from outside. It won't get recycled? Then such device needs to get hot from dissipating that heat.

? I think you are very confused. Yes, there is conservation of energy, but not conservation of entropy. See the second law of thermodynamics