feat: add role-specific statistics to telemetry and UI (cont. #15234) (#18824)

Co-authored-by: Yuna Seol <yunaseol@google.com>

packages/core/src/services/loopDetectionService.ts

@@ -25,6 +25,7 @@ import {
   isFunctionResponse,
 } from '../utils/messageInspectors.js';
 import { debugLogger } from '../utils/debugLogger.js';
+import { LlmRole } from '../telemetry/types.js';
 
 const TOOL_CALL_LOOP_THRESHOLD = 5;
 const CONTENT_LOOP_THRESHOLD = 10;
@@ -554,6 +555,7 @@ export class LoopDetectionService {
         abortSignal: signal,
         promptId: this.promptId,
         maxAttempts: 2,
+        role: LlmRole.UTILITY_LOOP_DETECTOR,
       });
 
       if (