fix: switch to PostHogProvider per official React integration guide (#112)

- Install @posthog/react and wrap app with PostHogProvider
- Use VITE_PUBLIC_POSTHOG_KEY and VITE_PUBLIC_POSTHOG_HOST env vars
- Use defaults: '2026-01-30' for recommended settings
- Remove manual initAnalytics() call — Provider handles initialization
- Analytics module now checks posthog.__loaded for readiness

Co-authored-by: Claude Opus 4.6 (1M context) <noreply@anthropic.com>

frontend/package.json

@@ -25,6 +25,7 @@
     "@dnd-kit/sortable": "^10.0.0",
     "@dnd-kit/utilities": "^3.2.2",
     "@monaco-editor/react": "^4.7.0",
+    "@posthog/react": "^1.8.2",
     "@sentry/react": "^10.42.0",
     "@sentry/vite-plugin": "^5.1.1",
     "@stripe/stripe-js": "^8.7.0",