What is God's relationship to people who are in hell?

God's wrath remains on them (John 3:36). If you believe, you have eternal life. Whoever does not obey the Son, the wrath of God abides on them. And I presume that means forever. So God is infinitely angry at people in hell forever.

He is separate from them, in that they are not allowed to enjoy any of his grace and beauty.

Outer darkness is a phrase that I think, probably, is meant to communicate a realm of existence that in no way contaminates the new heavens and the new earth, so that the totality of reality as we know it in the future, in the new heavens and the new earth, is totally good, totally beautiful, and totally free from sin.

And where they are, those who are excluded, is outer—it's outside this magnificent creation that God has made here. It's a strange relationship: it's out there. I don't believe in annihilationism. And I don't believe that it will be some pocket within the new heavens and the new earth. It will be outside.

But the main thing to say about the relationship is that it is one in which they hate him and he is infinitely wrathful towards them forever.