Fix tracing of async cursors for psycopg

This copies the traced_execution of AsyncCursorTracer except
query_method is awaited within the span.

Fixes #2486

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

@@ -149,7 +149,7 @@
 from opentelemetry.instrumentation.instrumentor import BaseInstrumentor
 from opentelemetry.instrumentation.psycopg.package import _instruments
 from opentelemetry.instrumentation.psycopg.version import __version__
-from opentelemetry.trace import TracerProvider
+from opentelemetry.trace import SpanKind, TracerProvider
 
 _logger = logging.getLogger(__name__)
 _OTEL_CURSOR_FACTORY_KEY = "_otel_orig_cursor_factory"
@@ -381,6 +381,46 @@ def callproc(self, *args: Any, **kwargs: Any):
     return TracedCursorFactory
 
 
+class AsyncCursorTracer(CursorTracer):
+    async def traced_execution(
+        self,
+        cursor: dbapi.CursorT,
+        query_method: Callable[..., Any],
+        *args: tuple[Any, ...],
+        **kwargs: dict[Any, Any],
+    ):
+        name = self.get_operation_name(cursor, args)
+        if not name:
+            name = (
+                self._db_api_integration.database
+                if self._db_api_integration.database
+                else self._db_api_integration.name
+            )
+
+        with self._db_api_integration._tracer.start_as_current_span(
+            name, kind=SpanKind.CLIENT
+        ) as span:
+            if span.is_recording():
+                if args and self._commenter_enabled:
+                    if self._enable_attribute_commenter:
+                        # sqlcomment is added to executed query and db.statement span attribute
+                        args = self._update_args_with_added_sql_comment(
+                            args, cursor
+                        )
+                        self._populate_span(span, cursor, *args)
+                    else:
+                        # sqlcomment is only added to executed query
+                        # so db.statement is set before add_sql_comment
+                        self._populate_span(span, cursor, *args)
+                        args = self._update_args_with_added_sql_comment(
+                            args, cursor
+                        )
+                else:
+                    # no sqlcomment anywhere
+                    self._populate_span(span, cursor, *args)
+            return await query_method(*args, **kwargs)
+
+
 def _new_cursor_async_factory(
     db_api: DatabaseApiAsyncIntegration | None = None,
     base_factory: type[psycopg.AsyncCursor] | None = None,
@@ -395,7 +435,7 @@ def _new_cursor_async_factory(
             tracer_provider=tracer_provider,
         )
     base_factory = base_factory or psycopg.AsyncCursor
-    _cursor_tracer = CursorTracer(db_api)
+    _cursor_tracer = AsyncCursorTracer(db_api)
 
     class TracedCursorAsyncFactory(base_factory):
         async def execute(self, *args: Any, **kwargs: Any):