Add PostHog analytics — full event tracking across all pages

Tracks pageviews, hero/CTA clicks, product teaser clicks, app card
and detail views, newsletter signups, nav interactions, and footer
link clicks with structured properties for PostHog dashboards.

Co-Authored-By: Claude Sonnet 4.6 <noreply@anthropic.com>

package.json

@@ -9,16 +9,17 @@
     "lint": "next lint"
   },
   "dependencies": {
+    "next": "14.2.35",
+    "posthog-js": "^1.396.4",
     "react": "^18",
-    "react-dom": "^18",
-    "next": "14.2.35"
+    "react-dom": "^18"
   },
   "devDependencies": {
-    "typescript": "^5",
     "@types/node": "^20",
     "@types/react": "^18",
     "@types/react-dom": "^18",
     "postcss": "^8",
-    "tailwindcss": "^3.4.1"
+    "tailwindcss": "^3.4.1",
+    "typescript": "^5"
   }
 }