cargo run -p bootstrap -- test tidy fails because it can't find the sysroot

[jyn514]

I tried this:

cargo run -p bootstrap -- test tidy

I expected to see this happen: Tidy runs fine, just as if I'd run x test tidy.

Instead, this happened:

Building stage0 tool tidy (x86_64-unknown-linux-gnu(x86_64-unknown-linux-gnu))
   Compiling itoa v0.4.6
   Compiling lazy_static v1.4.0
   Compiling regex-syntax v0.6.25
   Compiling same-file v1.0.6
   Compiling cfg-if v1.0.0
   Compiling memchr v2.4.1
   Compiling ryu v1.0.5
   Compiling serde v1.0.125
error[E0463]: can't find crate for `core`

error[E0463]: can't find crate for `compiler_builtins`

error[E0463]: can't find crate for `core`
 --> /home/jnelson/.local/lib/cargo/registry/src/github.com-1ecc6299db9ec823/lazy_static-1.4.0/src/inline_lazy.rs:8:1
  |
8 | extern crate core;
  | ^^^^^^^^^^^^^^^^^^ can't find crate

error[E0463]: can't find crate for `std`
 --> /home/jnelson/.local/lib/cargo/registry/src/github.com-1ecc6299db9ec823/lazy_static-1.4.0/src/inline_lazy.rs:9:1
  |
9 | extern crate std;
  | ^^^^^^^^^^^^^^^^^ can't find crate

The problem is that src/bootstrap/build.rs is setting RUSTC to ~/.cargo/bin/rustc, not ~/.rustup/toolchains/beta-x86_64-unknown-linux-gnu/bin/rustc, which breaks because rustbuild then can't find the appropriate sysroot.

cc #92260

@rustbot label: +A-bootstrap