Yes, I tried to use Cursor as an editor. Terrible idea in hindsight.
So your workflow now looks like mine except I prefer a different editor and only use the latest and greatest model so Cursor basically offers nothing over Codex.
I disagree about prompt engineering, but it's one of those things that probably varies because of what language you use, what problems you solve, and the degree to which you care about the output. Unless I'm writing tests, I keep AI on a very short leash because I'm writing critical code used by a very large number of users. I have noticed big differences in output quality depending on how I steer AI. Without steering, it will happily leave in dead code, change the use of variables so they need to be renamed, assume or fail to assume invariants, etc. As I said in another comment, I think we won't need to do that for very much longer, but right now it seems essential.