Run the tests from std in the CI

This will probably be done in a similar way to [how we do the UI tests](https://github.com/rust-lang/rustc_codegen_gcc/blob/06d07f816a9e95de360c95cabca907bd6e666905/build_system/src/test.rs#L1080-L1094), but using the command [to run the tests of the standard library](https://rustc-dev-guide.rust-lang.org/tests/running.html#run-tests-on-the-standard-library).