Resolve "Generated plot config backup does not include `plot_func` and `module` entries"

This MR fixes a bug that prohibited recreating a plot from the plot config file saved alongside the plot output.

Can this MR be accepted?

• Implementation ready
• Tests added or adjusted
• Documentation extended or updated

• Code quality
  • Changes follow coding guidelines
  • Checked code coverage on new and adjusted code

• Ready for merging
  • Pipeline passes without warnings
  • History cleaned-up or squash option set
  • Changelog entry added
  • Version number bumped

Related issues

Closes #320 (closed)