add error as context["exception"] in InProcessTestSupervisor

task-sdk/src/airflow/sdk/execution_time/supervisor.py

@@ -1680,6 +1680,7 @@ def start(  # type: ignore[override]
                 log = structlog.get_logger(logger_name="task")
 
                 state, msg, error = run(ti, context, log)
+                context["exception"] = error
                 finalize(ti, state, context, log, error)
 
                 # In the normal subprocess model, the task runner calls this before exiting.