Remove #![feature(let_chains)] from library and src/librustdoc
PR https://github.com/rust-lang/rust/pull/132833 has stabilized the `let_chains` feature. This PR removes the last occurences from the library, the compiler, and librustdoc (also because #140887 missed the conditional in one of the crates as it was behind the "rustc" feature).
We keep `core` as exercise for the future as updating it is non-trivial (see PR thread).