feat: Add coordinator log viewer to cluster UI

- Created /api/cluster/logs endpoint to read coordinator.log
- Added real-time log display in cluster UI (updates every 3s)
- Shows last 100 lines of coordinator.log in terminal-style display
- Includes manual refresh button
- Improves debugging experience - no need to SSH for logs

User feedback: 'why dont we add the output of the log at the bottom of the page so i know whats going on'

This addresses poor visibility into coordinator errors and failures.
Next step: Fix SSH timeout issue blocking worker execution.

app/cluster/page.tsx

@@ -56,6 +56,8 @@ export default function ClusterPage() {
   const [error, setError] = useState<string | null>(null)
   const [controlLoading, setControlLoading] = useState(false)
   const [controlMessage, setControlMessage] = useState<string | null>(null)
+  const [coordinatorLog, setCoordinatorLog] = useState<string>('')
+  const [logLoading, setLogLoading] = useState(false)
 
   const fetchStatus = async () => {
     try {
@@ -71,6 +73,21 @@ export default function ClusterPage() {
     }
   }
 
+  const fetchLog = async () => {
+    try {
+      setLogLoading(true)
+      const response = await fetch('/api/cluster/logs')
+      const data = await response.json()
+      if (data.success) {
+        setCoordinatorLog(data.log)
+      }
+    } catch (error) {
+      console.error('Failed to fetch coordinator log:', error)
+    } finally {
+      setLogLoading(false)
+    }
+  }
+
   const handleControl = async (action: 'start' | 'stop') => {
     setControlLoading(true)
     setControlMessage(null)
@@ -94,8 +111,13 @@ export default function ClusterPage() {
 
   useEffect(() => {
     fetchStatus()
-    const interval = setInterval(fetchStatus, 30000) // Refresh every 30s
-    return () => clearInterval(interval)
+    fetchLog()
+    const statusInterval = setInterval(fetchStatus, 30000) // Refresh status every 30s
+    const logInterval = setInterval(fetchLog, 3000) // Refresh log every 3s
+    return () => {
+      clearInterval(statusInterval)
+      clearInterval(logInterval)
+    }
   }, [])
 
   if (loading) {
@@ -211,6 +233,28 @@ export default function ClusterPage() {
           </div>
         </div>
 
+        {/* Coordinator Log */}
+        <div className="bg-gray-900 rounded-lg p-6 border border-gray-800">
+          <div className="flex items-center justify-between mb-4">
+            <h3 className="text-lg font-semibold">Coordinator Log</h3>
+            <button
+              onClick={fetchLog}
+              disabled={logLoading}
+              className="px-3 py-1 bg-gray-800 hover:bg-gray-700 rounded text-sm disabled:opacity-50"
+            >
+              {logLoading ? '⏳ Loading...' : '🔄 Refresh'}
+            </button>
+          </div>
+          <div className="bg-black rounded-lg p-4 overflow-auto max-h-96">
+            <pre className="text-xs text-green-400 font-mono whitespace-pre-wrap">
+              {coordinatorLog || 'No log output available'}
+            </pre>
+          </div>
+          <div className="mt-2 text-xs text-gray-500">
+            Updates automatically every 3 seconds
+          </div>
+        </div>
+
         {/* Worker Details */}
         <div className="grid grid-cols-1 md:grid-cols-2 gap-6 mb-6">
           {status.workers.map((worker) => (