Add Sitemap lastmod Support Using File Timestamps

Summary

The sitemap generator in packages/content/src/sitemap.ts currently emits no <lastmod> tags. With $file.modified available in the content pipeline, sitemap generation can include <lastmod> for each page, helping search engines prioritize crawl frequency.

Acceptance Criteria

• Sitemap XML output includes <lastmod> elements for pages that have a file.modified value
• <lastmod> uses ISO 8601 date format (YYYY-MM-DD)
• Pages without a modification date omit <lastmod> rather than emitting an empty element
• Existing sitemap output structure (URL, priority, changefreq if present) is unaffected
• Test verifying <lastmod> appears in sitemap output when file timestamps are available

Approach

1. In packages/content/src/sitemap.ts, read file.modified from page data during serialization
2. Emit <lastmod> element within the <url> block when the value is present
3. Add test case

References

• File-Derived Timestamps for Runes (Broader Impact — Sitemap)
• Inject $file.created and $file.modified Variables into Content Pipeline (variable injection — dependency)
• packages/content/src/sitemap.ts — sitemap generator