PR summary

This is a rebase of #11863 with the addition of a test. That PR was closed because #16082 defaulted animations to save intermediate files to a temporary directory. However, that didn't actually fix the ability to pass arguments to setup, which means the idea from #16082 to "just pass frame_prefix if you want to save the temporary files" was never possible.

PR checklist

• [n/a] "closes #0000" is in the body of the PR description to link the related issue
• new and changed code is tested
• [n/a] Plotting related features are demonstrated in an example
• New Features and API Changes are noted with a directive and release note
• Documentation complies with general and docstring guidelines