Thats the question. Even if wormholes exist, the Universe is under no obligation to make them observable to us. If they are always on the other side of a black hole event horizon, then there would be no way for us to detect them, even in principle.
/s (Sort of.. not really)
You can't have that all in a single star system.
Frankly I find that whole set up only slightly more plausible than some kind of FTL, especially since they also have gravity manipulation tech already.
That said recent talks about habitable zone around a black hole made me wonder if that would work.
Good point.
Perhaps in the far future there will be a Find a wormhole challenge where future human teenagers will dive their spaceships into a blackhole they think is in fact the entrance to a wormhoe and scream YOLO just before entering the event horizon.