Allow redirecting subprocess stdout to our stderr etc. (redux)
This is the code from #88561, tidied up, including review suggestions, and with the for-testing-only CI commit removed. FCP for the API completed in #88561.
I have made a new MR to facilitate review. The discussion there is very cluttered and the branch is full of changes (in many cases as a result of changes to other Rust stdlib APIs since then). Assuming this MR is approvedl we should close that one.
### Reviewer doing a de novo review
Just code review these four commits.. FCP discussion starts here: https://github.com/rust-lang/rust/pull/88561#issuecomment-1640527595
Portability tests: you can see that this branch works on Windows too by looking at the CI results in #88561, which has the same code changes as this branch but with an additional "DO NOT MERGE" commit to make the Windows tests run.
### Reviewer doing an incremental review from some version of #88561
Review the new commits since your last review. I haven't force pushed the branch there.
git diff the two branches (eg `git diff 176886197d6..0842b69c219`). You'll see that the only difference is in gitlab CI files. You can also see that *this* MR doesn't touch those files.
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