Preserve elapsed time in replay activity parts

frontend/app/components/assistant-ui/thread-list.tsx

@@ -442,7 +442,7 @@ export function toReplayRepository(
 			id,
 			role: message.role,
 			createdAt: new Date(),
-			content: toThreadMessageContent(parts),
+			content: toThreadMessageContent(parts, elapsedMs),
 			...(message.role === "assistant"
 				? {
 						status: { type: "complete", reason: "stop" },
@@ -797,9 +797,11 @@ function attachStageNote(input: unknown, stageNote?: string) {
 	return { value: input, __claw_stage_note: note };
 }
 
-function toThreadMessageContent(parts: UIMessage["parts"]) {
+function toThreadMessageContent(parts: UIMessage["parts"], elapsedMs?: number) {
 	return parts.map((part) => {
-		if (part.type === "text" || part.type === "reasoning") return part;
+		const elapsedPayload = elapsedMs === undefined ? {} : { elapsedMs };
+		if (part.type === "text") return part;
+		if (part.type === "reasoning") return { ...part, ...elapsedPayload };
 		if (part.type === "dynamic-tool") {
 			return {
 				type: "tool-call",
@@ -807,6 +809,7 @@ function toThreadMessageContent(parts: UIMessage["parts"]) {
 				toolCallId: part.toolCallId,
 				args: part.input ?? {},
 				argsText: JSON.stringify(part.input ?? {}),
+				...elapsedPayload,
 				...(part.state === "output-available" ? { result: part.output } : {}),
 			};
 		}