Realistically, I think NASA is hoping that SpaceX and probably also Blue Origin will create LEO space stations and lunar surface bases that NASA can buy rides and space in. That makes sense, so long as there is some other source of funding for SpaceX besides NASA and probably the US Space Force. I can see NASA and other science entities creating a lunar base on the far side for astronomy research.
Regarding Mars exploration, clearly NASA is not going to send astronauts one-way. But, if Musk has some takers for one-way trips, I can see NASA and/or others paying for them to do specific science tasks when they are there.
But, at some point, there will probably be newer engine technology for the trip between Earth and Mars, so all of this focus on the limitations of the current StarShip design are not making much of an impression on me about long-term limitations.
And, even before anybody sends people to Mars, it seems that Musk will be sending something like the StarShip there. And, that seems to make some sense for NASA to buy a ride for some really big robotic payloads. I expect that to be a lot cheaper for NASA than its current SLS program. SpaceX is already launching payloads to Europa, so why not to Mars?