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 (andpytest passes).
• IsFlake 8 compliant (runflake8 on changed files to check).
• New features are documented, with examples if plot related.
• Documentation is sphinx and numpydoc compliant (the docs shouldbuild without error).
• Conforms to Matplotlib style conventions (installflake8-docstrings andpydocstyle<4 and runflake8 --docstring-convention=all).
• New features have an entry indoc/users/next_whats_new/ (follow instructions in README.rst there).
• API changes documented indoc/api/next_api_changes/ (follow instructions in README.rst there).