[clang] [llvm] [clang][ci] Move libc++ testing into the main PR pipeline (PR #93318)

[Louis Dionne via cfe-commits]

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ldionne wrote:

I did check and it can be removed. I wrote that script so hopefully I’m not mistaken!

I will also go and clean up (remove the clang-ci pipeline on Buildkite, since it’s not used anymore). I will wait a week begore doing so to avoid breaking any ongoing PR that might trigger it.

https://github.com/llvm/llvm-project/pull/93318