Some demons mate for life; others take mates as it appeals to them. Sesshomaru is of the latter variety. For now. There might come a day when he is more like his father.

"We did not speak much." so there are many - many - things he doesn't know, "Zhou Zishu, keep her safe." because he had been afraid something bad at befallen her.

And he won't seek her out. Not if she doesn't want to be found. That is her right.