The mystery of 13x13 Volume 3 How should white defend on the top right coner?

At this moment, white defending the top right is a great move, but how to defend?

In the real game, white played the two space extension, it seems to be a good move to limit black's development, but AI think there is better ways.

AI suggested white to play white 1, because after black 2, white has the tesuji.

White advanced into black's territory easily with the tesuji.

AI also think the knight move is not as good as the diagonal move.

The reason is knight move could provide the opportunity for black to leverage strength.