Fix thread-safety in `get_local_type_info()` (#5856)

Fixes potential thread-safety issues if types are concurrently
registered while `get_local_type_info()` is called in free threaded
Python.

Use the `internals` mutex to also protect `local_internals`. This
keeps the locking strategy simpler, and we already follow this pattern
in some places, such as `pybind11_meta_dealloc`.