Conscious while asleep?

Seems when we fall asleep, we are no longer conscious. But when we are placed under anesthesia, we are unconscious in a much more extreme way; there is no continuity when we again wake up.

Our mind works even when we are not conscious. For example, we are working on a problem, but give up. Days later the answer comes to us. Is there a sense in which that part of our mind solving the problem was conscious?

Certainly we are not conscious of the workings of our internal organs. But is our soul residing in the spiritual realm conscious of such things?

And what about other creatures such as ants? Are they conscious more than we might imagine via their souls residing in the spiritual realm?

I'm beginning to suspect our awareness of our own consciousness is incomplete; that our soul residing in the spiritual realm is more conscious than we are. This implies two foci of awareness; one limited to our brain, and the other in our soul residing in the spiritual realm. After death, the soul "wakes up".

Perhaps it works in an analogous manner as the Trinity; one essence, multiple conscious persons?