Auto merge of #145131 - Kobzol:bootstrap-clippy, r=jieyouxu

Enforce in bootstrap that clippy must have stage at least 1

This mostly piggybacks on the previous `x check` [rework](https://github.com/rust-lang/rust/pull/143048).

The new "rules" follow the new staging logic. So `x clippy <foo>` lints `foo` using stage0 Clippy. `x clippy --stage 2 <foo>` lints `foo` using stage1 Clippy (which is built from in-tree sources).

I had to fix some latent issues with `prepare_compiler_for_check` along the way.

Checking `rustc_private` tools should now check less compiler crates (or rather not check compiler examples/tests/etc.), potentially speeding it up slightly.

I also had to make some manual adjustments to `x clippy ci` so that it doesn't do needless work.

r? `@jieyouxu`