Humanize run transcripts across run detail and live surfaces

Co-Authored-By: Paperclip <noreply@paperclip.ing>

packages/adapters/cursor-local/src/ui/parse-stdout.ts

@@ -142,6 +142,12 @@ function parseAssistantMessage(messageRaw: unknown, ts: string): TranscriptEntry
         kind: "tool_call",
         ts,
         name,
+        toolUseId:
+          asString(part.tool_use_id) ||
+          asString(part.toolUseId) ||
+          asString(part.call_id) ||
+          asString(part.id) ||
+          undefined,
         input,
       });
       continue;
@@ -199,6 +205,7 @@ function parseCursorToolCallEvent(event: Record<string, unknown>, ts: string): T
       kind: "tool_call",
       ts,
       name: toolName,
+      toolUseId: callId,
       input,
     }];
   }