auto-claude: subtask-2-3 - Add web-vitals reporting to layout for Core Web Vitals monitoring

- Create WebVitals client component in src/components/analytics/
- Track LCP, INP, CLS, FCP, and TTFB metrics
- Log metrics to console in development mode
- Send metrics to Google Analytics when available
- Add WebVitals component to root layout

Co-Authored-By: Claude Opus 4.5 <noreply@anthropic.com>

src/components/analytics/WebVitals.tsx

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+'use client';
+
+import { useEffect } from 'react';
+import { onCLS, onINP, onLCP, onFCP, onTTFB, type Metric } from 'web-vitals';
+
+type WebVitalsReportHandler = (metric: Metric) => void;
+
+interface WebVitalsProps {
+  /**
+   * Optional custom report handler. If not provided, metrics are logged to console in development.
+   */
+  onReport?: WebVitalsReportHandler;
+}
+
+/**
+ * Reports Core Web Vitals metrics.
+ *
+ * Metrics tracked:
+ * - LCP (Largest Contentful Paint): measures loading performance
+ * - INP (Interaction to Next Paint): measures interactivity
+ * - CLS (Cumulative Layout Shift): measures visual stability
+ * - FCP (First Contentful Paint): measures time to first content
+ * - TTFB (Time to First Byte): measures server response time
+ */
+export function WebVitals({ onReport }: WebVitalsProps) {
+  useEffect(() => {
+    const handleMetric: WebVitalsReportHandler = (metric) => {
+      if (onReport) {
+        onReport(metric);
+      } else if (process.env.NODE_ENV === 'development') {
+        // Log metrics in development for debugging
+        const { name, value, rating, id } = metric;
+        // eslint-disable-next-line no-console
+        console.log(`[Web Vitals] ${name}: ${value.toFixed(2)} (${rating}) [${id}]`);
+      }
+
+      // Send to Google Analytics if available
+      if (typeof window !== 'undefined' && 'gtag' in window) {
+        const gtag = window.gtag as (
+          command: string,
+          eventName: string,
+          params: Record<string, unknown>
+        ) => void;
+
+        gtag('event', metric.name, {
+          event_category: 'Web Vitals',
+          event_label: metric.id,
+          value: Math.round(metric.name === 'CLS' ? metric.value * 1000 : metric.value),
+          non_interaction: true,
+        });
+      }
+    };
+
+    // Register all Core Web Vitals observers
+    // Each function returns an unsubscribe function, but web-vitals v5 doesn't require cleanup
+    // as it uses PerformanceObserver internally which is garbage collected
+    onCLS(handleMetric);
+    onINP(handleMetric);
+    onLCP(handleMetric);
+    onFCP(handleMetric);
+    onTTFB(handleMetric);
+  }, [onReport]);
+
+  // This component doesn't render anything
+  return null;
+}

src/components/analytics/index.ts

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+export { WebVitals } from './WebVitals';