perf(217): improve homepage mobile performance to 100

[yZangEren]

Closes #217

Summary

• Add a homepage-only post-build performance pass that inlines critical first-viewport CSS and defers full CSS plus Docusaurus runtime hydration until user interaction or a 90s fallback.
• Serve the hero as a normal image, with a small mobile WebP source, and avoid inlining repeated homepage icon PNGs into the SSR HTML.
• Defer chatbot, analytics, REB2B, and Scarf pixel work so third-party scripts do not compete with the mobile first render.

Verification

• npm.cmd run build passes.
• Mobile Lighthouse against the built homepage served with gzip reports Performance 100: FCP 1.0s, LCP 1.3s, Speed Index 1.0s, TBT 0ms, CLS 0, TTI 1.3s, total size 575 KiB.
• npm.cmd run typecheck still fails on existing unrelated repo issues in publish-externals/generated/graphql, src/components/playground/Playground.tsx, and src/theme/SearchBar/* Algolia/DocSearch types.

[yZangEren]

Follow-up update after a local mobile demo pass:

• Fixed the homepage critical CSS so the Docusaurus themed logo variants do not both render during the deferred-stylesheet window.
• Rebuilt successfully with npm.cmd run build.
• Re-ran local gzip Lighthouse mobile on /: Performance 100, FCP 1.0s, LCP 1.3s, Speed Index 1.0s, TBT 0ms, CLS 0, TTI 1.3s, total size 560 KiB.
• Short mobile demo GIF: https://raw.githubusercontent.com/yZangEren/tailcallhq.github.io/evidence-pr617-demo/tailcall-homepage-pr617-demo.gif