A Ringworld around our Sun at Earth’s distance with Earthlike gravity would rotate at (IIRC) 1.5 million kmh. The centrifugal forces would tear our apart.
A Dyson Swarm remains the most promising megastructure for creating efficient living area (per unit mass).
We know it's not indestructible (and can't be unless it's a fantasy novel with "magic"), I only read the first book and there were two large holes even in the tiny section they explored.
Whatever happens to that hole in the ring that they find when they first encounter and land - crash - on the ring? Air is constantly lost through it. Not the one with the ultra-high "mountain" near where they crashed, the other one further along their route with the weather pattern caused by this air-loss storm. How is that sustainable - given the ultra-long time horizon, surely billions of years, that such a structure should be able to support life for (if a planet can do that much)?
The terrible failure mode was typical for the extreme arrogance of the ringworld engineers.
I'm not so sure about that. Consider slicing the ring into sections. If the ring is at the same radius and velocity of an object in orbit, then the slices will (mostly) stay put. They aren't going to fly off radially. So connecting them will not put undue stress on them.
I say mostly because they'll be tugs from the other planets, etc.
So sure you could make a non-spinning ring that minimizes the tension, velocity, and centrifugal force, but it would not provide a large living area like the ringworld does.
What I don't know is if the sun was 1/16th as bright and physically smaller if that would bring the ring into the realm of physically possible.