How did the Court determine it had the authority to issue the writ without determining if said authority had been suspended pursuant to the Constitution?
How did the Court determine that its authority to issue the writ had not been suspended without determining who had the authority to suspend said authority pursuant to the Constitution?
The case before the court was not whether their power to issue the writ had been suspended. That implies that they did have the power but it was denied in this instance. No, the case was that they lacked the authority to issue the writ in the first place under any circumstances. And the court ruled that they did. Since habeas corpus had not been suspended then that wasn't an issue before the court. And since habeas corpus had not been suspended then the question of who may suspend it was certainly not an issue before the court.