DOC: README.md further maintenance

[cpelley]

Tasks

• Migrate some of the documentation from README.md to relevant Python modules (module documentation).
• Fluff out missing class/function/method/module docstrings.
• Ensure all docstrings are rendered correctly as markdown.
• Update call signature extract to accommodate non type defaults.

Issues

• https://github.com/MetOffice/improver_suite/issues/2079