Leonel spent some time with his brothers before returning to the Lab Setting. He didn't establish a connection with the outside world because that could lead to some issues, which was why he had taken so long to break the news to them and also why he hadn't really been communicating with Aina either.
The Force Arts the Gathering of Kingdoms worked on were far beyond what level King had been on, and before his recent breakthrough, King had practically been a suffocating influence to Leonel.
So, it wasn't Leonel's place to make large deductions about how everything worked. For all he knew, if he projected his voice to the outside world, then it would register Anastasia's world as part of the Gathering of Kingdoms and try to take hold of it.
While the Segmented Cube was the greatest treasure ever created by the best Crafting Race to ever exist, the Gathering of Kingdoms was literally created by the God Beasts of Creation. They still couldn't be compared.