Fix Pagefind file serving with API route

Fixed issue where Pagefind static files weren't accessible due to Next.js routing conflicts.

Solution:
- Created API route at app/pagefind/[...path]/route.ts to serve Pagefind files from .next/pagefind/
- Updated build script to copy pagefind index to public/_pagefind (backup)
- API route handles all /pagefind/* requests and serves files with proper content types
- Added caching headers for optimal performance

This resolves the "cannot type in search" issue - the search modal can now load Pagefind UI and index files correctly.

Technical Details:
- Next.js App Router was treating /pagefind/ as a route, returning 404
- Static files in public/ weren't accessible for subdirectories due to routing priority
- API route bypasses routing to serve .next/pagefind/* files directly
- Supports .js, .css, .json, .wasm, and Pagefind-specific file types

🤖 Generated with [Claude Code](https://claude.com/claude-code)

Co-Authored-By: Claude <noreply@anthropic.com>

package.json

@@ -6,7 +6,7 @@
   "scripts": {
     "dev": "concurrently \"contentlayer2 dev\" \"next dev\"",
     "sync-assets": "node scripts/sync-assets.mjs",
-    "build": "npm run sync-assets && contentlayer2 build && next build && npx pagefind --site .next",
+    "build": "npm run sync-assets && contentlayer2 build && next build && npx pagefind --site .next && rm -rf public/_pagefind && cp -r .next/pagefind public/_pagefind",
     "start": "next start",
     "lint": "next lint",
     "contentlayer": "contentlayer build"