By carefully tearing down components of LatexManager in the right order
(first the subprocess), we avoid the need for a global registry of
things that need to be cleared at process termination.

PR Summary

PR Checklist

• Has pytest style unit tests (and pytest passes).
• Is Flake 8 compliant (run flake8 on changed files to check).
• New features are documented, with examples if plot related.
• Documentation is sphinx and numpydoc compliant (the docs should build without error).
• Conforms to Matplotlib style conventions (install flake8-docstrings and pydocstyle<4 and run flake8 --docstring-convention=all).
• New features have an entry in doc/users/next_whats_new/ (follow instructions in README.rst there).
• API changes documented in doc/api/next_api_changes/ (follow instructions in README.rst there).