fix: improve step 2 email switch handling

tests/background-logging-status-module.test.js

@@ -15,3 +15,28 @@ test('logging/status module exposes a factory', () => {
 
   assert.equal(typeof api?.createLoggingStatus, 'function');
 });
+
+test('logging/status add-phone detection ignores step 2 phone-entry switch failures', () => {
+  const source = fs.readFileSync('background/logging-status.js', 'utf8');
+  const globalScope = {};
+  const api = new Function('self', `${source}; return self.MultiPageBackgroundLoggingStatus;`)(globalScope);
+
+  const loggingStatus = api.createLoggingStatus({
+    chrome: { runtime: { sendMessage() { return Promise.resolve(); } } },
+    DEFAULT_STATE: { stepStatuses: {} },
+    getState: async () => ({ stepStatuses: {} }),
+    isRecoverableStep9AuthFailure: () => false,
+    LOG_PREFIX: '[test]',
+    setState: async () => {},
+    STOP_ERROR_MESSAGE: 'stopped',
+  });
+
+  assert.equal(
+    loggingStatus.isAddPhoneAuthFailure('姝ラ 2锛氬綋鍓嶉〉闈粛鍋滅暀鍦ㄦ墜鏈哄彿杈撳叆妯″紡锛屾湭鎴愬姛鍒囨崲鍒伴偖绠辫緭鍏ユā寮忋€俇RL: https://chatgpt.com/'),
+    false
+  );
+  assert.equal(
+    loggingStatus.isAddPhoneAuthFailure('姝ラ 8锛氶獙璇佺爜鎻愪氦鍚庨〉闈㈣繘鍏ユ墜鏈哄彿椤甸潰锛屽綋鍓嶆祦绋嬫棤娉曠户缁嚜鍔ㄦ巿鏉冦€?URL: https://auth.openai.com/add-phone'),
+    true
+  );
+});