Rollup merge of #125218 - Oneirical:easy-test-the-third, r=jieyouxu

Migrate `run-make/no-intermediate-extras` to new `rmake.rs`

Part of #121876 and the associated [Google Summer of Code project](https://blog.rust-lang.org/2024/05/01/gsoc-2024-selected-projects.html).

Author: matthiaskrgr