Add PostHog analytics integration

.gitignore

@@ -7,3 +7,4 @@ playwright-report/
 .agents/
 .claude/
 .windsurf/
+.env.local

instrumentation-client.ts

@@ -0,0 +1,9 @@
+import posthog from "posthog-js";
+
+posthog.init(process.env.NEXT_PUBLIC_POSTHOG_PROJECT_TOKEN!, {
+  api_host: "/ingest",
+  ui_host: "https://us.posthog.com",
+  defaults: "2026-01-30",
+  capture_exceptions: true,
+  debug: process.env.NODE_ENV === "development",
+});

next.config.ts

@@ -5,6 +5,23 @@ const nextConfig: NextConfig = {
   images: {
     unoptimized: true,
   },
+  async rewrites() {
+    return [
+      {
+        source: "/ingest/static/:path*",
+        destination: "https://us-assets.i.posthog.com/static/:path*",
+      },
+      {
+        source: "/ingest/array/:path*",
+        destination: "https://us-assets.i.posthog.com/array/:path*",
+      },
+      {
+        source: "/ingest/:path*",
+        destination: "https://us.i.posthog.com/:path*",
+      },
+    ];
+  },
+  skipTrailingSlashRedirect: true,
 };
 
 export default nextConfig;