Rollup merge of #140966 - est31:let_chains_library, r=tgross35

Remove #![feature(let_chains)] from library and src/librustdoc

PR rust-lang/rust#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).

Author: fmease