opentelemetry-instrumentation-dbapi: suppress async cursor spans

.changelog/4622.fixed

@@ -0,0 +1 @@
+`opentelemetry-instrumentation-dbapi`: suppress async cursor spans when instrumentation is disabled

instrumentation/opentelemetry-instrumentation-dbapi/src/opentelemetry/instrumentation/dbapi/__init__.py

@@ -909,6 +909,9 @@ async def traced_execution_async(
         *args: tuple[Any, ...],
         **kwargs: dict[Any, Any],
     ):
+        if not is_instrumentation_enabled():
+            return await query_method(*args, **kwargs)
+
         operation_name = self.get_operation_name(cursor, args)
         name = operation_name
         if not name:

instrumentation/opentelemetry-instrumentation-dbapi/tests/test_dbapi_integration.py

@@ -525,6 +525,33 @@ def test_suppress_instrumentation(self):
         spans_list = self.memory_exporter.get_finished_spans()
         self.assertEqual(len(spans_list), 0)
 
+    def test_suppress_instrumentation_async(self):
+        db_integration = dbapi.DatabaseApiIntegration(
+            "instrumenting_module_test_name",
+            "testcomponent",
+        )
+        cursor_tracer = dbapi.CursorTracer(db_integration)
+        mock_cursor = MockCursor()
+        called = False
+
+        async def async_execute(_query, *_args):
+            nonlocal called
+            called = True
+
+        with suppress_instrumentation():
+            asyncio.run(
+                cursor_tracer.traced_execution_async(
+                    mock_cursor,
+                    async_execute,
+                    "Test query",
+                    ("param1Value", False),
+                )
+            )
+
+        spans_list = self.memory_exporter.get_finished_spans()
+        self.assertEqual(len(spans_list), 0)
+        self.assertTrue(called)
+
     def _get_metric(self, name):
         return next(
             (