It's no opinion, non-seq. It is a simple matter of fact about the document as written by the people who were there and as understood by any and all but the most tortured, willfully obtuse, and intentionally deceptive readings of that document's explicit text. If your argument were valid - which it is not - you would have to not only accepted an extremely tortured reading of the constitution but also explicitly deny the recorded understanding of that clause by the people who were physically there at the constitutional convention. In any case, such an argument is unsustainable, indefensible, and for all practical purposes junk.
Case in point: Robert Yates, a delegate to the Constitutional Convention, explicitly wrote of that clause that "In the same section it is provided, that "the privilege of the writ of habeas corpus shall not be suspended, unless when in cases of rebellion and invasion, the public safety may require it." This clause limits the power of the legislature to deprive a citizen of the right of habeas corpus, to particular cases viz. those of rebellion and invasion; the reason is plain, because in no other cases can this power be exercised for the general good."
Robert Yates was there at the convention, non-seq. Had the authors of the constitution considered even the remote possibility that the clause pertained to anybody other than Congress do you think that Yates would have said what he did? Do you honestly believe that Robert Yates or any of the other delegates to that convention - any single one of them - ever believed that the clause they wrote and they inserted into Article I under the explicit provisions of Article I applied to somebody other than Congress? If you do then not only do you possess great ignorance of your country's history - you are also willfully dishonest about it.
but not one shared by Abraham Lincoln.
The assertion that black people are equal to white people was not shared by Abraham Lincoln. Does that make it less true?
Since the Constitution does not explicitly state who may suspend habeas corpus then it would be for the Supreme Court to determine who is right.
Your premise is faulty. The Constitution DOES explicitly state who can suspend it and that body is Congress. Once again, exactly what about the phrase "All legislative Powers herein granted shall be vested in a Congress of the United States" is so confusing? Exactly what about that phrase do you not understand?
That phrase doesn't state that the suspension of habeus corpus is a legislative power, only that legislative powers are vested with congress, and your interpretation doesn't account for the extended periods when Congress is not in session.
Lincoln did pretty well given the secessionist cards he was dealt. For example in 1861 he could have leveled Charleston without suspending habeus corpus, and he didn't.
The Constitution does not state that.