[codex] Clean up homepage navigation assets

[Ridealist]

Summary

• Remove global MathJax loading from the shared head include so non-math pages avoid unnecessary script loading.
• Keep MathJax available through the existing use_math: true page path.
• Replace homepage optional Academicons mappings with Font Awesome fallbacks to avoid broken icons without adding another CDN.
• Fix favicon manifest and browserconfig icon paths to point at committed assets.

Validation

• bundle exec jekyll build
• git diff --check
• Verified homepage has no masthead/sidebar while category and post pages keep the existing masthead/sidebar.
• Verified MathJax is absent from home/category/non-math post pages and still present on /llm/fine-tuning-llm/.
• Verified manifest and browserconfig icon paths resolve to committed files.

Existing Sass deprecation warnings from Minimal Mistakes are still present.

Closes #11