fix(webui): preserve activity duration on replay

webui/src/components/thread/ThreadMessages.tsx

@@ -134,6 +134,7 @@ function reasoningOnlyMessageFromAnswer(message: UIMessage): UIMessage {
     reasoningStreaming: message.reasoningStreaming,
     isStreaming: message.reasoningStreaming,
     activitySegmentId: message.activitySegmentId,
+    latencyMs: message.latencyMs,
   };
 }
 
@@ -204,6 +205,8 @@ export function ThreadMessages({
           unit.type === "cluster"
           && next?.type === "single"
           && next.message.role === "assistant";
+        const turnLatencyMs =
+          unit.type === "cluster" ? activityClusterTurnLatencyMs(unit.messages, next) : undefined;
 
         return (
           <div key={unitKey(unit, index)} className={marginTop}>
@@ -212,6 +215,7 @@ export function ThreadMessages({
                 messages={unit.messages}
                 isTurnStreaming={index === liveActivityClusterIndex}
                 hasBodyBelow={hasBodyBelow}
+                turnLatencyMs={turnLatencyMs}
                 cliApps={cliApps}
                 mcpPresets={mcpPresets}
               />
@@ -234,6 +238,28 @@ export function ThreadMessages({
   );
 }
 
+function activityClusterTurnLatencyMs(
+  messages: UIMessage[],
+  next: DisplayUnit | undefined,
+): number | undefined {
+  for (let i = messages.length - 1; i >= 0; i -= 1) {
+    const latency = messages[i].latencyMs;
+    if (typeof latency === "number" && Number.isFinite(latency) && latency >= 0) {
+      return latency;
+    }
+  }
+  if (
+    next?.type === "single"
+    && next.message.role === "assistant"
+    && typeof next.message.latencyMs === "number"
+    && Number.isFinite(next.message.latencyMs)
+    && next.message.latencyMs >= 0
+  ) {
+    return next.message.latencyMs;
+  }
+  return undefined;
+}
+
 function currentActivityClusterIndex(units: DisplayUnit[]): number {
   const last = units.length - 1;
   return units[last]?.type === "cluster" ? last : -1;