Show last listing update time next to connection status in header

Add last_updated timestamp to /api/status endpoint by querying
MAX(last_seen) across both listing tables. Display it in the
HealthIndicator as relative time (e.g. "2h ago") with full
date/time in the tooltip on hover.

frontend/src/components/HealthIndicator.tsx

@@ -8,6 +8,20 @@ interface HealthIndicatorProps {
   interval?: number;
 }
 
+function formatRelativeTime(isoString: string): string {
+  const date = new Date(isoString);
+  const now = new Date();
+  const diffMs = now.getTime() - date.getTime();
+  const diffMins = Math.floor(diffMs / 60000);
+  const diffHours = Math.floor(diffMs / 3600000);
+  const diffDays = Math.floor(diffMs / 86400000);
+
+  if (diffMins < 1) return 'just now';
+  if (diffMins < 60) return `${diffMins}m ago`;
+  if (diffHours < 24) return `${diffHours}h ago`;
+  return `${diffDays}d ago`;
+}
+
 export function HealthIndicator({ interval = 30000 }: HealthIndicatorProps) {
   const [health, setHealth] = useState<HealthCheckResult>({ status: 'checking' });
 
@@ -46,12 +60,19 @@ export function HealthIndicator({ interval = 30000 }: HealthIndicatorProps) {
   };
 
   const getTooltipContent = () => {
+    const lines: string[] = [];
+
     if (health.status === 'checking') {
       return 'Checking backend connection...';
     }
 
     if (health.status === 'healthy') {
-      return `Backend connected (${health.latencyMs}ms)`;
+      lines.push(`Backend connected (${health.latencyMs}ms)`);
+      if (health.lastUpdated) {
+        const date = new Date(health.lastUpdated);
+        lines.push(`Last update: ${date.toLocaleString()}`);
+      }
+      return lines.join('\n');
     }
 
     return `Backend unavailable: ${health.error || 'Unknown error'}`;
@@ -72,10 +93,15 @@ export function HealthIndicator({ interval = 30000 }: HealthIndicatorProps) {
             <span className={`text-xs ${getStatusColor(health.status)} hidden sm:inline`}>
               {getStatusLabel(health.status)}
             </span>
+            {health.status === 'healthy' && health.lastUpdated && (
+              <span className="text-xs text-muted-foreground hidden sm:inline">
+                · {formatRelativeTime(health.lastUpdated)}
+              </span>
+            )}
           </div>
         </TooltipTrigger>
         <TooltipContent side="bottom">
-          <p>{getTooltipContent()}</p>
+          <p className="whitespace-pre-line">{getTooltipContent()}</p>
         </TooltipContent>
       </Tooltip>
     </TooltipProvider>

frontend/src/services/healthService.ts

@@ -6,6 +6,7 @@ export interface HealthCheckResult {
   status: HealthStatus;
   latencyMs?: number;
   error?: string;
+  lastUpdated?: string;
 }
 
 /**
@@ -39,6 +40,7 @@ export async function checkBackendHealth(): Promise<HealthCheckResult> {
       return {
         status: 'healthy',
         latencyMs,
+        lastUpdated: data.last_updated ?? undefined,
       };
     }