fix(dashboard): deduplicate realtime log replay

src/web/log-broadcaster.ts

@@ -22,16 +22,20 @@ export class LogBroadcaster {
   }
 
   push(level: LogEntry['level'], message: string, data?: unknown): void {
-    const entry: LogEntry = { timestamp: Date.now(), level, message, data };
+    const realtimeEvent = this.eventHub.closed
+      ? undefined
+      : this.eventHub.publish('log.created', { level, message, data });
+    const entry: LogEntry = {
+      timestamp: realtimeEvent ? Date.parse(realtimeEvent.occurredAt) : Date.now(),
+      level,
+      message,
+      data,
+    };
     this.entries.push(entry);
     if (this.entries.length > MAX_LOGS) {
       this.entries = this.entries.slice(-MAX_LOGS);
     }
 
-    if (!this.eventHub.closed) {
-      this.eventHub.publish('log.created', { level, message, data });
-    }
-
     this.fanout(JSON.stringify({ type: 'log', ...entry }));
   }