feat: add Core Web Vitals reporting to PostHog

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

frontend/src/lib/webVitals.ts

@@ -0,0 +1,35 @@
+/**
+ * Core Web Vitals reporting via PostHog.
+ *
+ * Tracks LCP, INP, CLS, FCP, and TTFB as PostHog events so we can
+ * build dashboards and correlate performance with product usage.
+ *
+ * Each metric fires once per page load. PostHog captures 100% of
+ * sessions (vs Sentry's 20% sample), giving better coverage.
+ */
+import { onLCP, onINP, onCLS, onFCP, onTTFB } from 'web-vitals'
+import type { Metric } from 'web-vitals'
+import posthog from 'posthog-js'
+
+function sendToPostHog(metric: Metric) {
+  // Only send if PostHog is loaded
+  if (!(posthog as unknown as { __loaded?: boolean }).__loaded) return
+
+  posthog.capture('web_vitals', {
+    metric_name: metric.name,
+    metric_value: metric.value,
+    metric_rating: metric.rating,
+    metric_delta: metric.delta,
+    metric_id: metric.id,
+    page_path: window.location.pathname,
+  })
+}
+
+/** Register all Web Vitals observers. Call once after PostHog init. */
+export function initWebVitals() {
+  onLCP(sendToPostHog)
+  onINP(sendToPostHog)
+  onCLS(sendToPostHog)
+  onFCP(sendToPostHog)
+  onTTFB(sendToPostHog)
+}