What if Boeing writes a report and NASA approves it in some manner. Is it then a NASA report? or not? or does it depend on type of approval?

Honestly no idea if this would be standard or not

If someone dies, or something goes wrong in a way that causes further hardware damage (during re-entry or during ISS proximity operations, for example), there definitely will be. We get reports in response to, say, Challenger or Columbia. When it's an FAA thing, we get mishap reports on stuff like IFT-3. But as best I can tell, the FAA doesn't have much jurisdiction or relevance to what's going wrong with Starliner. (Is there any chance I'm mistaken and we get an FAA mishap report instead? Should I update the language here to include that?)

And things are definitely off-nominal enough to have substantial agency impacts -- people are working overtime on things, and priorities have shifted strongly at relevant labs and test sites, in ways that impact other programs.

But does all that imply we'll get a report from it? I'm not sure either!

If Starliner deorbits and lands in the center of Times Square, I think that's an FAA matter. (Specifically I think reentry is FAA)

Do you think the question is more interesting / useful if I update it to include FAA or NASA?

What I was originally trying to go for was "do we get an official analysis on what went wrong" and I didn't really think about it maybe being the FAA that wrote it up.

Nah just responding to your specific question about what situation we might get an FAA report. I think the market is fine as is.
Would you count a GAO report? Not sure if that's applicable here, probably not.

I think a GAO report is unlikely to do anything about technical root cause analysis, or technical contributing factors, which is the thing I'm trying to get at.

Is the problem that Boeing failed to pass on requirements? That the thrusters did not meet requirements? Were the thrusters not adequately tested in an appropriate environment? Who should have known to do better testing? Did NASA program managers allow Boeing to skip tests because Boeing and Aerojet have good industry reputations? Etc.

(I had been thinking about writing questions like those in a multi-outcome question about "what will the Starliner report say", and then I realized I didn't know whether we'd get one!)

But I'm also on board with not changing the question even if I didn't quite manage to capture what I wanted.

I suspect this could use some workshopping on the resolution details; suggestions are welcome!

I will not trade until we have those details figured out.