[llvm] [libc++] Switch over to the LLVM-wide premerge test runners. (PR #147794)

[Aiden Grossman via llvm-commits]

boomanaiden154 wrote:

Just FYI: The container image we're using here is a bit of a hack given we needed to bump the runner binary version. I took the existing container, deleted the runner binary, and then reinstalled it and uploaded it to the registry so that we could use it:
```
FROM ghcr.io/llvm/libcxx-linux-builder:b060022103f551d8ca1dad84122ef73927c86512
RUN rm -rf ./*
ENV GITHUB_RUNNER_VERSION=2.326.0
RUN curl -O -L https://github.com/actions/runner/releases/download/v$GITHUB_RUNNER_VERSION/actions-runner-linux-x64-$GITHUB_RUNNER_VERSION.tar.gz && \
    tar xzf ./actions-runner-linux-x64-$GITHUB_RUNNER_VERSION.tar.gz && \
    rm ./actions-runner-linux-x64-$GITHUB_RUNNER_VERSION.tar.gz
```

This shouldn't be an issue when building the next container as #147831 has already landed

https://github.com/llvm/llvm-project/pull/147794