It placed restrictions on where it can be suspended, not who can suspend it. It addressed Congress in the case because habeas corpus had been suspended under powers granted by an act of Congress. The Supreme Court has never ruled on just who may suspend it because the matter has never been taken before the entire court. It should have been, in 1861, but it wasn't. The matter remains unresolved.
I agree that there was no controversy as to which branch of government had the authority to suspend the writ of habeas corpus. The President did not challenge the court on that point. But the Court clearly expressed the notion that the power lies with Congress first, and the presidnet acting alone only if and only for as long as Congress is unable to act.
The matter remains unresolved.
Your point seems to be that the president generally has the unilateral power to suspend habeas corpus (because the power is not granted to Congress, not denied to the executive), and until the Court says otherwise (and according to you, it didn't in the Milligan case), the president holds that power today.
I disagree with that, but have nothing further to offer in support. I think the Milligan case speaks well to the question.