If a Jupiter Trojan asteroid, (60deg before or after Jupiter in its 11.86yr orbit), such a settlement would have a disadvantage of becoming easily reachable from Earth just once/12yr, after its orbit had gradually gotten modified lots more elliptic so it would swing in near Earth's orbit, (then out near Saturn's orbit 6yr later). That altered orbit would be helpfully given some tilt relative to the planetary disk so that while between Earth and Saturn, it would pass safely above or below Jupiter and many asteroids.
There are lots of bigger asteroids in our Solar system, and lots more in the Kuiper belt about 6 times Neptune's distance from Sol, having over 100,000 of big size over 100km, and lots more of smaller sizes. And also there's the much bigger Oort cloud of asteroids well outside there, to distances like a light-year from Sol, (leaving little sensible reason to ever instead try a maybe centuries long trip seeking some remote star's imagined wished for though quite unlikely livable good planet).
Like for producing what had been needed for a Cylinder space settlement, a robotic collection would begin by refining asteroid materials to greatly expand its abilities. It would have brought a small Solar energy converting disk film. This would be expanded early as needed to supply ever more energy to refine ever more asteroid materials while producing more wanted equipment.
Eventually a bigger Solar energy collecting film would be formed as a disk put up on a polar tower and slowly spun, the facing direction kept facing Sol. Over time, even bigger disk films could be put up in front of an old one, with the old one then lowered to get expanded bigger to later replace the new one. A different tower could be anchored into the equator with a high ion jet to gradually slow and alter daily rotation. It could tilt the old axis to point at Sol, (perpendicular to the orbit axis), and give the asteroid an extremely slow new rotation "day" matching its orbit period, to have the slowly spinning Solar energy collecting disk film on its tower extremely slowly stay well facing Sol.
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