This is getting to metaphysics outside my training. The key thing for halting oracle is to be able to observe a true infinity. That is the challenge. The contradiction arises because the halting oracle, also, is a program subject to inclusion in a program itself.
In the case of God, both these two things might be side stepped. Perhaps God can create an infinite timeline outside himself, and observe all of it from outside that timeline. If that is the case, He could be a halting oracle without logical contradiction. Not that the halting oracle here is not subject to logical contradiction, because it can’t be called recursively as is required for the proof against halting oracles above. That is my sloppy attempt to show why God is not necessarily subject to the halting oracle logical contradiction.
Another solution could be that he just knows, without process or mechanism of knowing, he just knows. It is God after all, why not?
If God makes a rock so large no one else can lift it, and then He promises not to move it, than that rock is immovable to everyone including Him. Right?