Add a proper example to the "patch DAG" API documentation

[jakubczaplicki]

Since redoc seems to have a bug affecting the autogen documentation , and there's no ETA for fixing it, I propose a solution based on the workaround described in Redocly/redoc#1238

related: #19402
related: #15917

[boring-cyborg]

Congratulations on your first Pull Request and welcome to the Apache Airflow community! If you have any issues or are unsure about any anything please check our Contribution Guide (https://github.com/apache/airflow/blob/main/CONTRIBUTING.rst)
Here are some useful points:

• Pay attention to the quality of your code (flake8, mypy and type annotations). Our pre-commits will help you with that.
• In case of a new feature add useful documentation (in docstrings or in docs/ directory). Adding a new operator? Check this short guide Consider adding an example DAG that shows how users should use it.
• Consider using Breeze environment for testing locally, it’s a heavy docker but it ships with a working Airflow and a lot of integrations.
• Be patient and persistent. It might take some time to get a review or get the final approval from Committers.
• Please follow ASF Code of Conduct for all communication including (but not limited to) comments on Pull Requests, Mailing list and Slack.
• Be sure to read the Airflow Coding style.
  Apache Airflow is a community-driven project and together we are making it better 🚀.
  In case of doubts contact the developers at:
  Mailing List: [email protected]
  Slack: https://s.apache.org/airflow-slack

[github-actions]

The PR is likely OK to be merged with just subset of tests for default Python and Database versions without running the full matrix of tests, because it does not modify the core of Airflow. If the committers decide that the full tests matrix is needed, they will add the label 'full tests needed'. Then you should rebase to the latest main or amend the last commit of the PR, and push it with --force-with-lease.

[mik-laj]

Tested. Works!

[boring-cyborg]

Awesome work, congrats on your first merged pull request!