perf: enable lite-yt-embed, optimize avatar, add cache headers

- YouTube embeds now use lite-youtube facade (loads iframe on click,
  ~800 KiB savings per page with embedded videos)
- Avatar resized from 1000x1000 to 400x400 (152 KiB → 39 KiB)
- lite-yt-embed.css max-width changed to 100% for responsive layout
- Removed unused Tailwind primary color palette from CSS bundle

Confab-Link: http://localhost:8080/sessions/edb1b7b0-da66-4486-bd9c-d1cfa7553b88

tailwind.config.js

@@ -41,20 +41,6 @@ export default {
           900: "#78350f",
           950: "#451a03",
         },
-        // Legacy — kept for compatibility, not used in templates
-        primary: {
-          50: "#eff6ff",
-          100: "#dbeafe",
-          200: "#bfdbfe",
-          300: "#93c5fd",
-          400: "#60a5fa",
-          500: "#3b82f6",
-          600: "#2563eb",
-          700: "#1d4ed8",
-          800: "#1e40af",
-          900: "#1e3a8a",
-          950: "#172554",
-        },
       },
       fontFamily: {
         sans: [