I've almost completed rebuilding the World Destroyer. It's in someone else's system, and my construction ship has halted work for want of dilithium crystal. Is there any way to supply the construction ship with the materiel?
I've tried swapping the construction ships out, with no luck. I also can't order a privately owned cargo ship full of the stuff to supply my constructor.
It should happen automatically. In Shadows, I find that any missing resources in repairs to a World Destroyer project are delivered long before the work finishes, just because the repair takes an inordinate amount of time (caveat: I do not know what affects the time it takes; if it is connected with research speed, that is set to very slow in my games).
What you describe looks typical for earlier versions of the game.
It is also possible that the freighter which was assigned by the AI to transport Dilithium chose an insecure location to pick up the goods. The freighter may have been shooed away by pirates or similar. The game takes a while to recover from such interruptions. An affected freighter will usually take up another job and the AI takes its time to take on urgent jobs (most of the freighter fleet is busy with unimportant tasks). The good new is that in Shadows there should be eventually come another freighter.
If you have it in hand, you could build a Dilithium mine somewhere close to the construction site, closer than any other Dilithium source. Transport assignments will typically choose a source close to the target. With the construction site in foreign territory this may be difficult though. Getting a new mine built and wait for the AI to actually pick this as a source rather than someplace insecure may take a long time, anyway, or be entirely futile, though.
A usually quicker alternative is to interrupt the current repair and give a new repair order either this or a different constructor. With an almost completed World Destroyer project, nobody would like this idea.
You could select the constructor, zoom out very far and turn on the civilian ship vectors overlay for the galaxy map. If there is any freighter assigned to deliver goods to the constructor, its vector will be drawn in red. If the vector doesn't point directly to the constructor, the ship is on its way to pick up cargo. Just keep in mind, this view isn't guaranteed to show whether a transport is underway. I do not know to which extent it covers 'independent' freighters. And even your ship may be inside a system, about to pick up cargo, then the vector won't show in the galaxy map.