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

[Tom Stellard via llvm-commits]

https://github.com/tstellar commented:

Can we also delete https://github.com/llvm/llvm-project/blob/main/clang/utils/ci/buildkite-pipeline.yml

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