[v3-1-test] Add documentation for Airflow Ctl integration tests in contributing-docs (#59387)

contributing-docs/09_testing.rst

@@ -47,6 +47,9 @@ includes:
 * `Task SDK integration tests <testing/task_sdk_integration_tests.rst>`__ are specialized tests that verify
   the integration between the Apache Airflow Task SDK package and a running Airflow instance.
 
+* `Airflow Ctl integration tests <testing/airflow_ctl_integration_tests.rst>`__ are tests we run to verify
+  if the ``airflowctl`` command-line tool works correctly with a running Airflow instance.
+
 You can also run other kinds of tests when you are developing Airflow packages:
 
 * `Testing distributions <testing/testing_distributions.rst>`__ is a document that describes how to

contributing-docs/testing/airflow_ctl_tests.rst

@@ -0,0 +1,47 @@
+ .. Licensed to the Apache Software Foundation (ASF) under one
+    or more contributor license agreements.  See the NOTICE file
+    distributed with this work for additional information
+    regarding copyright ownership.  The ASF licenses this file
+    to you under the Apache License, Version 2.0 (the
+    "License"); you may not use this file except in compliance
+    with the License.  You may obtain a copy of the License at
+
+ ..   http://www.apache.org/licenses/LICENSE-2.0
+
+ .. Unless required by applicable law or agreed to in writing,
+    software distributed under the License is distributed on an
+    "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY
+    KIND, either express or implied.  See the License for the
+    specific language governing permissions and limitations
+    under the License.
+
+Airflow Ctl (airflowctl) Tests
+===============================
+
+This document describes how to run tests for the Airflow Ctl (airflowctl) command-line tool.
+
+Similar to other integration tests, the Airflow Ctl tests are run in the Breeze environment.
+The tests are using the `Docker Compose <../airflow-core/doc/howto/docker-compose/docker-compose.yaml>`__ and running a full working Airflow environment.
+These tests run on a scheduled basis in CI and can also be run locally using Breeze.
+We have them to ensure the ``airflowctl`` tool is working as expected and interacting with Airflow instances correctly.
+Airflow Ctl integration tests are located in the root directory of Apache Airflow project.
+
+.. note::
+
+   The integration tests ensure that the ``airflowctl`` tool behaves as expected when interacting with Airflow instances.
+   They validate the tool's functionality in a controlled environment, providing confidence in its reliability.
+
+Running Airflow Ctl Tests with Breeze
+-------------------------------------
+
+Firstly, checkout the tag or branch you want to run the tests on.
+Then, you can run the tests using the following command:
+
+.. code-block:: bash
+
+   breeze testing airflow-ctl-integration-test
+
+.. note::
+
+   The above command runs the integration tests for ``airflowctl`` in the Breeze environment.
+   Ensure that the correct tag or branch is checked out before executing the tests.