"I understand a proposed amendment to the Constitution—which amendment, however, I have not seen—has passed Congress, to the effect that the Federal Government shall never interfere with the domestic institutions of the States, including that of persons held to service ... holding such a provision to now be implied constitutional law, I have no objection to its being made express and irrevocable."
He plainly says that if the people, by virtue of their representatives in congress, enact such an amendment, HE HAS NO OBJECTION. That's not the same as an endorsement! That's saying he recognizes the will of the people.
If you had read Doris Kearns-Goodwin’s book or several other sources you would know that Lincoln not only knew about the Corwin Amendment - he orchestrated its passage through the northern dominated Congress with the necessary supermajority. As the de facto leader of the party it would hardly make sense that he would not have read the legislation as he claimed during his inaugural address. He also leaned on his political supporters to arrange its passage through a few state legislatures.
He was promoting it. If he didn't give a care one way or the other, what point to putting it in his inaugural address? Why sign the letters going out to the Governors? The President plays no role in constitutional amendments. Adding his signature notifies the governors that this amendment has his support.