Humans are moving out of the solar system. They are using a 1 million ton ship with 10,000 residents. It will be propelled by a solar sail. They need a Dyson sphere(wherever the Earth’s orbit does not cross it), and currently this is their design: A Dyson sphere powering 50 fusion reactors(that are supplied with starlifting), that power a laser. They need to figure out the most efficient heat-to-power converter. (Carnot, Rakine, solar panels). ANything with the best efficiency works.
I'm going to treat this question as if it's tagged Science-Fiction. I feel compelled to. On the Kardashev civilization scale humanity ranks about 0.7 and it's theorized that Dyson spheres would require a Kardashev II civilization. Consequently, we need a scientifically fictional answer to a question about a fictional problem.
As @ths mentions in his/her comment, you don't need fusion reactors. You already have the biggest fusion reactor that star system will ever see in the form of the central star. Using star lifting doesn't help you because every time you convert from one energy-generation-solution to another (e.g., the sun's a fusion reactor, but you take mass from it to fuel another fusion reactor...) you lose efficiency. The point of a Dyson sphere is to capture 100% of the star's energy for useful purposes without suffering additional losses.
From a story standpoint, it would make more sense to lift mass from the star to act as fuel for star ships — something away from the Dyson sphere where it can't benefit directly from it.
I say "energy." You said "heat." What we're really talking about are photons and charged particles. Curiously, I've not personally seen an explanation of how to make a Dyson sphere work for protecting the inner shell from those high energy particles. Earth has the Van Allen radiation belts. I suppose you could have magnetic field generators all over the inner surface that channel all the particles somewhere useful, but I digress....
From a practical perspective, you're handwaving a lot of science in your world just to have Dyson spheres. We don't know how to construct them. We don't know how to manage them. They're a hypothetical idea that's uber cool and feeds the imagination. But that means that imagination is required to answer your question.
Wherever you're not using the inner surface for inhabitable land mass, you'll want some form of solar panel. For the sake of a science fiction story, call them solar accumulators or photon absorbers or some other cool synonym for "solar panels." In a very real sense, it won't matter if they're particularly efficient. Even using today's efficiencies (22%-26% on average, if I recall) you're talking about far more energy than you'd need to create the laser to propel your ships.
Note #1: Perfect efficiency is godlike. It would be unbelievable to me to suggest a K=2 civilization could/would have perfect efficiency. That means you are creating heat (the difference between the energy output of the sun and the energy you can capture is expressed as heat). You can do things with the heat, like heat water to drive steam turbines or somehow use a Seebeck thermoelectric generator (the problem is where to get the cold reference... not as easy as you might think in outer space)... but there will always be some left over. Your Dyson sphere will need big mother hubbard radiating fins to get rid of it.
Note #2: stay away from "Carnot" and "Rankine." While something about those thermodynamic cycles could be applied here, their primary purpose is to describe the means of converting heat into mechanical energy (think "combustion engines"), which you don't need.
If you wish to have better efficiency, do so! I can easily imagine that a K=2 civilization will have more efficient methods of converting photons and high energy particles to something useful — like electricity. And that's assuming they're still using electricity (that's the problem with trying to be "realistic" with K>=2 civilizations... we try not to make god in our own image, but it's a honking hard thing to avoid).
Have I answered your question?
Probably not... Kardashev's original publication estimated it would take humanity 3,200 years to reach level II, so you're asking us o apply 21st century technology to solve a 341st century problem. Authors avoid explaining details like this for a reason. It's really easy to be entirely wrong. I salute your desire to be realistic — but Dyson spheres aren't realistic (at least, not yet). Therefore, I'll conclude with a frame challenge: when setting the technological rules for your fictional world, focus on how the technology is used, not what the technology is or how it operates.
For the life of me, I can't remember the story writing term. Someone help me out here. It's not "gaslighting...." Rats, I hate getting old. What you'll likely end up doing to "explain" your photon-to-electricity conversion technology is write a one-or-two line bit of nonsense that helps inform the reader that you're not trying to use wholly science-based solutions (which is a good thing, because you can't).
A great example comes from the movie That Age of Adeline (2015). The writer wants to tell a love story about a woman hiding the fact that she's not aging — but the writer knows better than to try to scientifically explain how that can happen (it would be shot down quickly), so instead the writer states:
(Adeline's car slides off a wintry road into a body of water.) The immersion in the fridgid water caused Adeline's body to go into an anoxic reflex, instantly stopping her breathing and slowing her heartbeat. Within two minutes, Adeline Bowman's core temperature had dropped to 87 degrees. Her heart stopped beating. At 8:55 a bolt of lightning struck the vehicle, discharging half a billion volts of electricity and producing 60,000 amperes of current.
It's effect was three-fold:
First, the charge defibrillated Adeline Bowmans' heart. Second, she was jolted out of her anoxic state, causing her to draw her first breath in two minutes. Third, based on Von Layman's Principle of Electron Compression in Deoxyribonucleic Acid, which will be discovered in the year 2035, Adeline Bowman will henceforth be immune to the ravages of time. She will never age another day.
What's important about what you just read? Almost none of it is scientifically possible. Much of it isn't even scientifically plausible. And that last bit is pure technobabble. But that's what makes the whole explanation work. It's a clever way of placing a cool-sounding label that completely hides how the "technology" operates. The writers set a rule for their world and explained how it was used, which allowed them to move on to the story they wanted to tell.
It was excellent worldbuilding. How can I tell? Because people have been asking the Internet if it's real since the movie was released. (You'd think the 2035 date would give away the fiction... but people be people.)