`./x dist --stage 2 $tool` broken after #138224

[pietroalbini]

Creating distribution tarballs of tools with ./x dist --stage 2 $tool broke after #138224. We (Ferrocene) know it fails at least with rustfmt and clippy. From what I can see, it stopped building the stage1 library, causing that failure.

Build log before the PR got merged:

Building bootstrap
    Finished `dev` profile [unoptimized] target(s) in 0.07s
Building stage0 library artifacts (x86_64-unknown-linux-gnu)
    Finished `release` profile [optimized] target(s) in 0.05s
Building compiler artifacts (stage0 -> stage1, x86_64-unknown-linux-gnu)
    Finished `release` profile [optimized] target(s) in 0.26s
Creating a sysroot for stage1 compiler (use `rustup toolchain link 'name' build/host/stage1`)
Building stage0 tool lld-wrapper (x86_64-unknown-linux-gnu)
    Finished `release` profile [optimized] target(s) in 0.12s
Building stage1 library artifacts (x86_64-unknown-linux-gnu)
    Finished `release` profile [optimized] target(s) in 0.03s
Building compiler artifacts (stage1 -> stage2, x86_64-unknown-linux-gnu)
    Finished `release` profile [optimized] target(s) in 0.24s
Building tool clippy-driver (stage1 -> stage2, x86_64-unknown-linux-gnu)
   Compiling clippy v0.1.87 (/home/pietro/r/github/rust-lang/rust/master/src/tools/clippy)
   Compiling clippy_lints v0.1.87 (/home/pietro/r/github/rust-lang/rust/master/src/tools/clippy/clippy_lints)

Build log after the PR got merged:

Building bootstrap
   Compiling bootstrap v0.0.0 (/home/pietro/r/github/rust-lang/rust/master/src/bootstrap)
    Finished `dev` profile [unoptimized] target(s) in 5.83s
Building stage0 library artifacts (x86_64-unknown-linux-gnu)
    Finished `release` profile [optimized] target(s) in 0.10s
Building compiler artifacts (stage0 -> stage1, x86_64-unknown-linux-gnu)
    Finished `release` profile [optimized] target(s) in 0.33s
Creating a sysroot for stage1 compiler (use `rustup toolchain link 'name' build/host/stage1`)
Building stage0 tool lld-wrapper (x86_64-unknown-linux-gnu)
    Finished `release` profile [optimized] target(s) in 0.20s
Building tool clippy-driver (stage1 -> stage2, x86_64-unknown-linux-gnu)
   Compiling proc-macro2 v1.0.93
   Compiling unicode-ident v1.0.14
   Compiling serde v1.0.217
   Compiling stable_deref_trait v1.2.0
   Compiling litemap v0.7.4
   Compiling writeable v0.5.5
   Compiling smallvec v1.13.2
   Compiling icu_locid_transform_data v1.5.0
   Compiling icu_properties_data v1.5.0
   Compiling utf8_iter v1.0.4
   Compiling equivalent v1.0.1
   Compiling write16 v1.0.0
   Compiling icu_normalizer_data v1.5.0
   Compiling utf16_iter v1.0.5
   Compiling hashbrown v0.15.2
   Compiling rustc_apfloat v0.2.2+llvm-462a31f5a5ab
error[E0463]: can't find crate for `std`
  |
  = note: the `x86_64-unknown-linux-gnu` target may not be installed
  = help: consider adding the standard library to the sysroot with `x build library --target x86_64-unknown-linux-gnu`
  = help: consider building the standard library from source with `cargo build -Zbuild-std`

For more information about this error, try `rustc --explain E0463`.
error[E0463]: can't find crate for `core`
  |
  = note: the `x86_64-unknown-linux-gnu` target may not be installed
  = help: consider adding the standard library to the sysroot with `x build library --target x86_64-unknown-linux-gnu`
  = help: consider building the standard library from source with `cargo build -Zbuild-std`

error: could not compile `proc-macro2` (build script) due to 1 previous error
warning: build failed, waiting for other jobs to finish...
error: could not compile `unicode-ident` (lib) due to 1 previous error
error: could not compile `serde` (build script) due to 1 previous error
error: could not compile `icu_locid_transform_data` (lib) due to 1 previous error
error: could not compile `litemap` (lib) due to 1 previous error
error: could not compile `stable_deref_trait` (lib) due to 1 previous error
error: could not compile `icu_properties_data` (lib) due to 1 previous error
error: could not compile `write16` (lib) due to 1 previous error
error: could not compile `equivalent` (lib) due to 1 previous error
error: could not compile `utf8_iter` (lib) due to 1 previous error
error: could not compile `writeable` (lib) due to 1 previous error
error: could not compile `smallvec` (lib) due to 1 previous error
error: could not compile `icu_normalizer_data` (lib) due to 1 previous error
error: could not compile `utf16_iter` (lib) due to 1 previous error
error: could not compile `rustc_apfloat` (build script) due to 1 previous error
error: could not compile `hashbrown` (lib) due to 1 previous error
Build completed unsuccessfully in 0:00:08

[onur-ozkan]

I have the fix but I want to add a test coverage for #138004 before sending a PR. I'm hoping to do that in a couple of hours (don't have time atm).