Rollup merge of #94806 - jyn514:cargo-run-tidy, r=Mark-Simulacrum

Rollup merge of #94806 - jyn514:cargo-run-tidy, r=Mark-Simulacrum

Fix `cargo run tidy`

When I implemented rust-only bootstrapping in https://github.com/rust-lang/rust/pull/92260,
I neglected to test stage0 tools - it turns out they were broken because
they couldn't find the sysroot of the initial bootstrap compiler.

This fixes stage0 tools by using `rustc --print sysroot` instead of assuming rustc is already in a
sysroot and hard-coding the relative directory.

Fixes https://github.com/rust-lang/rust/issues/94797 (properly, without having to change rustup).