Auto merge of #124753 - GuillaumeGomez:migrate-rustdoc-determinism, r…

…=jieyouxu

Migrate `run-make/rustdoc-error-lines` to new `rmake.rs`

Part of rust-lang/rust#121876.

There was a weird naming inconsistency with `input`/`output`. A few tests write `.arg("-o").arg(path)` and the `output` method was actually the command output. So instead, I renamed the original `output` into `command_output` so that I could create the `output` method with the expected effect (and updated the tests to use it too).

EDIT: The first two commits come from rust-lang/rust#124711. Some weird things happened recently pparently. ^^'

r? `@jieyouxu`