[libcxx] [llvm] WIP: Experiment with improving the buildkite triggering (PR #122468)

[Louis Dionne via llvm-commits]

ldionne wrote:

I give up. I think I'd have to define the buildkite trigger in a `pull_request_target` event, but then that makes it impossible to order these checks after the rest of our pipeline like we want, which defeats the purpose.

https://github.com/llvm/llvm-project/pull/122468