Rollup merge of #121237 - Urgau:better-cargo-heuristic, r=compiler-errors

Use better heuristic for printing Cargo specific diagnostics

It was [reported](https://github.com/rust-lang/rust/issues/82450#issuecomment-1948574677) in the check-cfg call for testing that the Rust for Linux project is setting the `CARGO` env without compiling with it, which is an issue since we are using the `CARGO` env as a proxy for "was launched from Cargo".

This PR switch to the `CARGO_CRATE_NAME` [Cargo env](https://doc.rust-lang.org/cargo/reference/environment-variables.html#environment-variables-cargo-sets-for-crates), which shouldn't collide (as much) with other build systems. I also took the opportunity to consolidate all the checks under the same function.

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