Fix formatting for removed lints
- Don't add backticks for the reason a lint was removed. This is almost
never a code block, and when it is the backticks should be in the reason
itself.
- Don't assume clippy is the only tool that needs to be checked for
backwards compatibility
I split this out of https://github.com/rust-lang/rust/pull/80527/ because it kept causing tests to fail, and it's a good change to have anyway.
r? `@flip1995`