[Feature] Add button 'Copy Page as markdown for LLMs'

[zxkane]

I confirm:

• I have read the Hugo Clarity theme documentation.
• I have reviewed other issues in this repository, and this feature has not already been requested.

Type of feature (check all that apply)

• Site functionality
• Design (styling)
• Site performance
• Accessibility
• Translations and internationalization (i18n)
• Code improvements
• Other (please describe below)

Describe the feature

The LLM would benefit significantly from receiving the site content as Markdown, even if the source material is also Markdown.

Sample site with this capability: https://modelcontextprotocol.io/specification/2025-06-18/basic

Preferred solution

No response

Alternatives

No response

Additional Context

No response