Most of the debris is in low orbits. So no direct problem.
But if you build it in low earth orbit and fly it out on its own power in a slow spiral, then it's going to be a big problem. Flying with chemical rockets only up to LEO and electric propulsion from there on saves mass hugely.
Best to assemble moderate pieces and fly them higher after completion.
It wouldn't cast an umbral shadow at all. It would cast a incredibly faint penumbral shadow.
Look at it this way, at the sizes that are commonly talked about for these, at the orbital heights being talked about, the occlusion of the sun would be on the order of a very minor sun spot, and only for very brief periods of time.