perf: replace real-time polling with SSE streaming

Replace 5-second setInterval polling with EventSource connection to the
new /realtime/stream SSE endpoint. The server pushes visitor updates
instead of each client independently polling. Auto-reconnects on
connection drops.

lib/hooks/useRealtimeSSE.ts

@@ -0,0 +1,53 @@
+// * SSE hook for real-time visitor streaming.
+// * Replaces 5-second polling with a persistent EventSource connection.
+// * The backend broadcasts one DB query per site to all connected clients,
+// * so 1,000 users on the same site share a single query instead of each
+// * triggering their own.
+
+import { useEffect, useRef, useState, useCallback } from 'react'
+import { API_URL } from '@/lib/api/client'
+import type { Visitor } from '@/lib/api/realtime'
+
+interface UseRealtimeSSEReturn {
+  visitors: Visitor[]
+  connected: boolean
+}
+
+export function useRealtimeSSE(siteId: string): UseRealtimeSSEReturn {
+  const [visitors, setVisitors] = useState<Visitor[]>([])
+  const [connected, setConnected] = useState(false)
+  const esRef = useRef<EventSource | null>(null)
+
+  // Stable callback so we don't recreate EventSource on every render
+  const handleMessage = useCallback((event: MessageEvent) => {
+    try {
+      const data = JSON.parse(event.data)
+      setVisitors(data.visitors || [])
+    } catch {
+      // Ignore malformed messages
+    }
+  }, [])
+
+  useEffect(() => {
+    if (!siteId) return
+
+    const url = `${API_URL}/api/v1/sites/${siteId}/realtime/stream`
+    const es = new EventSource(url, { withCredentials: true })
+    esRef.current = es
+
+    es.onopen = () => setConnected(true)
+    es.onmessage = handleMessage
+    es.onerror = () => {
+      setConnected(false)
+      // EventSource auto-reconnects with exponential backoff
+    }
+
+    return () => {
+      es.close()
+      esRef.current = null
+      setConnected(false)
+    }
+  }, [siteId, handleMessage])
+
+  return { visitors, connected }
+}