fix: use explicit posthog.init() with client prop for reliable initialization (#113)

Switch from apiKey+options pattern to explicit posthog.init() before
render, then pass client instance to PostHogProvider. This is more
reliable and matches the PostHog SDK docs' recommended client pattern.

Enables autocapture and pageview tracking per PostHog defaults.

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

frontend/src/main.tsx

@@ -1,5 +1,6 @@
 import "./instrument"; // Sentry must init before any other imports
 
+import posthog from 'posthog-js'
 import { StrictMode } from 'react'
 import { createRoot } from 'react-dom/client'
 import { reactErrorHandler } from '@sentry/react'
@@ -9,10 +10,17 @@ import { Toaster } from 'sonner'
 import './index.css'
 import App from './App'
 
-const posthogOptions = {
-  api_host: import.meta.env.VITE_PUBLIC_POSTHOG_HOST || 'https://us.i.posthog.com',
-  defaults: '2026-01-30',
-} as const
+// Initialize PostHog client before rendering
+const posthogKey = import.meta.env.VITE_PUBLIC_POSTHOG_KEY as string | undefined
+if (posthogKey) {
+  posthog.init(posthogKey, {
+    api_host: (import.meta.env.VITE_PUBLIC_POSTHOG_HOST as string) || 'https://us.i.posthog.com',
+    autocapture: true,
+    capture_pageview: true,
+    capture_pageleave: 'if_capture_pageview',
+    persistence: 'localStorage+cookie',
+  })
+}
 
 createRoot(document.getElementById('root')!, {
   onUncaughtError: reactErrorHandler(),
@@ -20,10 +28,7 @@ createRoot(document.getElementById('root')!, {
   onRecoverableError: reactErrorHandler(),
 }).render(
   <StrictMode>
-    <PostHogProvider
-      apiKey={import.meta.env.VITE_PUBLIC_POSTHOG_KEY || ''}
-      options={posthogOptions}
-    >
+    <PostHogProvider client={posthog}>
       <HelmetProvider>
         {/* Toast notification system - theme syncs automatically via CSS custom properties */}
         <Toaster