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>

app/pagefind/[...path]/route.ts

@@ -0,0 +1,40 @@
+import { NextRequest, NextResponse } from 'next/server';
+import { readFile } from 'fs/promises';
+import { join } from 'path';
+
+export async function GET(
+  request: NextRequest,
+  { params }: { params: Promise<{ path: string[] }> }
+) {
+  try {
+    const { path } = await params;
+    const filePath = join(process.cwd(), '.next', 'pagefind', ...path);
+
+    // Read the file
+    const file = await readFile(filePath);
+
+    // Determine content type
+    const ext = path[path.length - 1].split('.').pop();
+    const contentTypes: Record<string, string> = {
+      'js': 'application/javascript',
+      'css': 'text/css',
+      'json': 'application/json',
+      'wasm': 'application/wasm',
+      'pf_meta': 'application/octet-stream',
+      'pf_index': 'application/octet-stream',
+      'pf_fragment': 'application/octet-stream',
+    };
+
+    const contentType = contentTypes[ext || ''] || 'application/octet-stream';
+
+    return new NextResponse(file, {
+      headers: {
+        'Content-Type': contentType,
+        'Cache-Control': 'public, max-age=31536000, immutable',
+      },
+    });
+  } catch (error) {
+    console.error('Error serving Pagefind file:', error);
+    return new NextResponse('File not found', { status: 404 });
+  }
+}