Auto merge of #100576 - joboet:movable_const_remutex, r=Mark-Simulacrum

Make `ReentrantMutex` movable and `const`

As `MovableMutex` is now `const`, it can be used to simplify the implementation and interface of the internal reentrant mutex type. Consequently, the standard error stream does not need to be wrapped in `OnceLock` and `OnceLock::get_or_init_pin()` can be removed.