Fix another false positive

Added corresponding test

Author: JessicaBell00

tools/pylint-extensions/azure-pylint-guidelines-checker/tests/test_files/do_not_log_exceptions.py

@@ -62,12 +62,18 @@ def test_other_logging_fails():
             return False
 
 
-# test_no_logging_ok
-def test_no_logging_ok():
+# test_no_logging_and_no_exception_name_ok
+def test_no_logging_and_no_exception_name_ok():
     try:
         add = 1 + 2
     except Exception as ex:
         self.errors.appendleft(ex)
+    except Exception as ex:  # pylint: disable=broad-except
+        _logger.warning(
+            "Exception occurred when instrumenting: %s.",
+            lib_name,
+            exc_info=ex,
+        )
 
 
 # test_logging_without_exception_name

tools/pylint-extensions/azure-pylint-guidelines-checker/tests/test_pylint_custom_plugins.py

@@ -5392,7 +5392,7 @@ def test_other_logging_fails(self, setup):
         ):
             self.checker.visit_try(try_node)
 
-    def test_no_logging_ok(self, setup):
+    def test_no_logging_and_no_exception_name_ok(self, setup):
         """Check that no logging is ok in the exception block."""
         try_node = setup.body[6].body[0]
         with self.assertNoMessages():