build(deps): update Astro and reduce dependency graph

[HDauven]

Summary

• upgrade Astro 6.0.8 to 7.1.3, Starlight 0.38.2 to 0.41.4, Sharp 0.34.5 to 0.35.3, and the link validator 0.20.1 to 0.25.2
• remove the unused remark-math and rehype-mathjax integration; no live documentation contains math syntax
• preserve Astro 6's compressHTML: true behavior explicitly across the Astro 7 upgrade
• pin all four required direct dependencies exactly
• enforce a seven-day package release floor and registry-only dependency sources
• install without lifecycle scripts, verify registry signatures, then rebuild only [email protected]
• use read-only GitHub Actions permissions without persisted checkout credentials

The resulting clean Linux installation falls from 377 to 363 packages. It removes the MathJax and @xmldom/xmldom chain and reports zero npm audit findings, so it should clear all 34 currently open Dependabot alerts after merge.

Compatibility

• all 59 generated content pages retain identical titles, normalized visible content, heading structure, links, code-block counts, and table counts versus main
• desktop and mobile comparisons across representative routes are visually identical apart from a 0.002-0.013% desktop pixel change in Starlight's sidebar disclosure icon
• search, tabs, theme options, and the mobile sidebar retain their existing behavior
• Starlight 0.41's supported browser floor is Chromium 111, Safari/iOS 16.4, and Firefox 121

Verification

• 469 lockfile entries across 459 registry packages pass the seven-day release-age check
• all 363 installed packages have verified registry signatures
• only [email protected] declares a lifecycle script
• Astro builds all 59 pages and optimizes all 14 image assets
• Starlight link validation passes for all internal links
• npm audit: 0 findings