So I'm making a post-FTL world in which humans are the first, and so far only, species to explore the stars. It's thousands (if not millions) of years in the future, and we've become post scarcity. Antimatter, Antienergy, Fusion, Fission, genetic engineering, molecular 3D printing, and FTL light travel have all been developed and perfected. Basically the only thing we can't do is manipulate gravity freely.
What form does my space habitat take to house the largest population of humans in a world where the limiting factors are only the forces of gravity vs structural integrity?
No Handwavium material, but feel free to create structures completely out of carbon nanotubes, gallium, gold, or any other material provided it won't decay fast enough to hurt structural integrity or irradiate people to death.
Structure should be made to last 1,000 years minimum.
Any given enclosure need to be connected to another enclosure with a walkway that can be walked through in a manageable amount of time, like an hour or less. It's a quirk that future humans have, wanting to be as closely together as possible.
It should be expandable when possible.
Logistics such as food, water, and electricity are all self contained in any given structure using '(S)ignificantly (A)dvanced (T)echnology [that it] appear[s]to be magic.' No need to worry about it I'll work around whatever.
Any size planet, black hole, or other astronomical body can be found and moved or made using S.A.T., so long as the body can exist at all. I.E.: Any star with enough mass to collapse into a black hole will, but any star below that size can be found and used.
Radiation coming from space is neutralized. However, if you use something radioactive like a sun in your design, you need to account for the mass of appropriate radiation shields.
Construction time is no object.
Given these perameters, how do I make the larges livable habitat possible?
Some possible forms the station could take:
An orb that encircles a black hole to use for gravity.
A series of super dense planetary cores that creates gravity for each consecutive floor building outwards in layers that encircle the entire planet until gravity is too weak, and then the outermost layer is connected to the outermost layer of another structure build around a planetary core.
A hollow cylinder surrounding the barycenter of a series of planets that all give off ~1g.
I am only looking for the calculations regarding structural integrity, and maximizing size of living space. It doesn't matter how I'm going to make it, I just want to know what shape I should make it in.