`--print=native-static-libs` is not emitted to `stdout`, but instead to `stderr`

Running the following:

$ echo "" > empty.rs
$ rustc empty.rs --crate-type=staticlib --print=native-static-libs
note: Link against the following native artifacts when linking against this static library. The order and any duplication can be significant on some platforms.

note: native-static-libs: -lSystem -lc -lm

I.e. it does produce the expected native-static-libs: ... note, but the note is emitted to the stderr stream, instead of stdout, as is done by the other --print=... flags.

I expected to be able to pipe the output to e.g. grep to extract the note, but no such luck:

$ rustc empty.rs --crate-type=staticlib --print=native-static-libs | grep native-static-libs

Meta

rustc --version --verbose:

rustc 1.80.0-nightly (e82c861d7 2024-05-04)
binary: rustc
commit-hash: e82c861d7e5ecd766cb0dab0bf622445dec999dc
commit-date: 2024-05-04
host: aarch64-apple-darwin
release: 1.80.0-nightly
LLVM version: 18.1.4

Start by reproducing the rustc empty.rs --crate-type=staticlib --print=native-static-libs command and trace the --print=native-static-libs handling in rustc. Compare its output stream with other --print flags, then verify that the native-static-libs note can be captured from stdout while the existing content remains correct.