feat(site): new home page, docs, and design system (#566)

Co-authored-by: Darius Cepulis <dcepulis@mux.com>
Co-authored-by: Claude Opus 4.6 <noreply@anthropic.com>

package.json

@@ -31,6 +31,7 @@
     "link:aliases": "node scripts/link-aliases.mjs",
     "size": "node .github/scripts/bundle-size.js | node .github/scripts/bundle-size-report.js",
     "test": "turbo run test",
+    "format:astro": "prettier --write 'site/src/**/*.astro'",
     "typecheck": "tsc --build"
   },
   "devDependencies": {
@@ -43,6 +44,9 @@
     "@types/node": "^22.18.6",
     "esbuild": "^0.27.3",
     "lint-staged": "^16.2.3",
+    "prettier": "^3.8.1",
+    "prettier-plugin-astro": "^0.14.1",
+    "prettier-plugin-tailwindcss": "^0.7.2",
     "react": "^18.0.0",
     "react-compiler-runtime": "^1.0.0",
     "react-dom": "^18.0.0",
@@ -56,6 +60,7 @@
     "commit-msg": "pnpm commitlint"
   },
   "lint-staged": {
+    "*.astro": "prettier --write",
     "*": "biome check --write --no-errors-on-unmatched"
   }
 }