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

[via llvm-commits]

cmtice wrote:

> This looks ready to me.
> 
> Once it's converted from a draft, I'll add my stamp.

Done -- it's ready for official review now. :-)

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