[libc++] Remove old CI configurations and update the supported compiler versions

`_LIBCPP_REMOVE_TRANSITIVE_INCLUDES` doesn't do anything anymore in C++23 mode, so it's now just a duplicate of the C++23 configuration.
Also add new steps to the post-release checklist for updating the supported compilers.

Reviewed By: ldionne, #libc

Spies: arichardson, libcxx-commits, arphaman

Differential Revision: https://reviews.llvm.org/D133364