Rollup merge of #117679 - aDotInTheVoid:yes-core, r=GuillaumeGomez

tests/rustdoc-json: Avoid needless use of `no_core` and `lang_items`

See #117487 for motivation.

I've split it into three commits, depending on how much work it was to remove `#![no_core]`. The first is entirely mechanical, the second makes no logical changes but couldn't be done with find+replace, and the third required rewriting assertions no not depend on having `#![no_core]`. All of the interesting changes for review are in the third commit, so I recommend reviewing commit-by-commit.

After this, 3 tests still use `#![no_core]`:

- `./tests/rustdoc-json/primitives/primitive_impls.rs`. Uses impls on primitives, so needs to simulate core
- `./tests/rustdoc-json/primitives/local_primitive.rs`: Uses `rustc_doc_primitive`, so needs to simulate core
- `./tests/rustdoc-json/impls/auto.rs`: Uses auto traits, so needs to simulate core

But after this change, we only rely on the core-rustc boundary in tests that deliberately test those interactions.

r? ``@GuillaumeGomez``

Fixes #117487

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