[libcxx] [llvm] [libc++][CI] Add hermetic Linux premerge builder (PR #226358)

[Aiden Grossman via llvm-commits]

https://github.com/boomanaiden154 commented:

This setup with an additional container image seems a bit fragile. If someone accidentally adds an additional dependency or something there, you'll never catch it.  Needing an additional container image for this is also a bit annoying.

Also, do you have examples of previous patches that have caused issues with such configurations?

https://github.com/llvm/llvm-project/pull/226358