I'm imagining a complete partitioning of utility functions here. To me, a type-II civilization would be more akin to the planet of the Matrix movies—a symbiotic system involving:

A. a sentient civilization, living in a virtual universe with unlimited possibility, and

B. a completely automated outer reality, keeping the sim running, of which the sentients have (and need) no awareness.

Part of the sentients' remembered history would be that that "we used to live in a much more limited universe, but then we ascended to this one," or something like that. The "reality" that the automated system inhabits would be no more real to the sentients than your fingertip is to your IDE. (And would have as little realization of an orbital bombardment against the automation as your IDE has of your fingertip holding down the power button of your computer.)

The automated system would want only to grow and maintain itself, and would not have the higher-level thinking capacity required to formulate larger goals. It would be more like a plant, having the same sort of relationship to the sentients that we have to bacteria that live in our bloodstreams. (I want to mention both Avatar and [End of] Evangelion here, for oddly-complementary visuals.)

I would think that even such a technologically dominant civilization would want to keep a few sentinels in the base reality. If only to keep an eye out for stray existential threats. And such a sentinel would be a fascinating character to base the narrative around; aware of the true nature of things, given vastly consequential powers in physical reality, but for all that, but not particularly important in the view of the society running inside.

True (I sort of had the feeling that this is why the Great Machine in Babylon 5 required an operator.)

But when you start to think like a post-Singularity sentient, you start to realize that their ethical system would be much "pickier" than ours. They would see leaving any of their own (whether biological or AI-based) in the "limited" reality as a punishment equal in scope to the suffering child of Omelas—that is to say, one they could not possibly stand for.