[libcxx] [llvm] [libc++] Add support for picolibc and newlib in RUNTIMES_USE_LIBC (PR #147956)

[Louis Dionne via llvm-commits]

https://github.com/ldionne approved this pull request.

> I think the only outstanding question above was if we needed to provide compatibility with the old way and a warning.

I am personally neutral on that check. I'm fine with your current patch.

LGTM as-is assuming the CI is green. Apologies for the review delay.

https://github.com/llvm/llvm-project/pull/147956