chore(snippet_manager): update HTML documentation with modern Docutils styles

This commit refreshes the generated HTML documentation for the snippet_manager module by:
- Updating to Docutils 0.22.3 with modern CSS3 styles
- Replacing deprecated XHTML syntax with HTML5
- Adding responsive design with viewport meta tag
- Implementing improved typography and spacing
- Enhancing accessibility with proper semantic HTML5 elements
- Maintaining all existing content while improving visual presentation

The changes ensure the documentation renders consistently across modern browsers while maintaining all existing functionality and content structure.

Author: janikvonrotz