The Buildings Are Self-Contained
For an in-depth discussion I recommend the <PERSON> episode on arcologies - self-sufficient structures with all their utilities, and most of their own economy, built in.
In essence, an arcology is a space habitat constructed on the ground. Another way to think of it is a city in a can. Waste is recycled internally so water supply is not an issue, food is often grown internally (this only needs fusion power or sufficiently advanced bioengineering, not magic tech), and everything that can be provided inside the building is. You don't need Star Trek style replicators - just living space for the people who work there, a reasonable supply of commonly needed technicians, tools, and spare parts, and the equivalent of an Amazon fulfillment center in there somewhere.
Compared to a space habitat, an arcology doesn't have to be quite so self-sufficient, and at least it doesn't have to be airtight. But much of the design is similar, because you don't want too many people or goods coming and going. Just as you can live your entire life inside a city today without really having to leave, you would be able to live your entire life inside an arcology if you wanted to.
The essential problem with traditional skyscrapers at extremely large scale is that the consumption requirements of the building increase with the building's volume, but the ability to get material in and out of the building increases only with the building's surface area. Forget the view from the top floor - the entire outer shell of the building has to be a loading dock or a garage! In concepts that don't involve ubiquitous flying vehicles, everything going in and out of the building has to pass through not only the edge of the building but the ground floor, so the available rate of material flow is essentially fixed, and buildings can't get much bigger than they are now. We already have trouble with traffic getting in and out of skyscrapers during rush hour periods. The design of elevator shafts for supertall buildings is already a serious problem and designers are inventing new ways to deal with it. So you keep everything inside the building that you can.
A facility for disposal of waste heat becomes the main external utility that an arcology must connect to, especially one that has its own fusion power plant. Even present-day skyscrapers have to run their air conditioners in the dead of winter, and city centers are hotter than the surrounding environments, in part because of heat generated in large buildings. 87
For arcologies, air-cooled heat pumps aren't going to cut it. Something like a molten sodium cooling loop would be more useful.
In some ways the construction architecture of arcologies parallels computer architecture. Early computers (say 1970s to mid-1980s) handled relatively little data and the CPU could communicate with memory and peripherals at its own speed. CPUs got faster and RAM cache had to be invented so the CPU didn't spend most of its time waiting on system RAM. Later CPUs got more and more levels of RAM cache of varying speeds because the cache needed its own cache. Eventually RAM and peripherals started to move directly onto the CPU itself and we now have integrated systems-on-chips including everything but the power and human interface components. Most of the actual space inside the chip is used just for storage or moving signals from place to place, not actual computations. And the essential limiting factor on performance is power in and heat out.
The development of arcologies can be evolutionary, not revolutionary. One example of something that's on the path to an arcology is the MIT campus. It's possible to travel almost anywhere on campus without going outside, like most universities it provides basic living needs to the students, and it even has its own power plant. Of course, it's not really self sufficient - they still need to bring in almost everything from outside - but it probably feels self-sufficient to the students that live there. Arcology-like architecture has also been proposed for the upcoming Amazon HQ2 - even if it's not contained in a single tall building. 284