Fix TaskHandlerWithCustomFormatter now adds prefix only once

[TiDeane]

When using the TaskHandlerWithCustomFormatter to add a prefix to logs, it was previously adding the prefix multiple times. This happened because its set_context method was being called multiple times from logging_mixin.py's set_context, and worsened because even when the handler's formatter was a TimezoneAware formatter (to include UTC offset), it was still adding an additional prefix. Because of this, I felt that any solution outside of the TaskHandlerWithCustomFormatter itself would either require a restructuring of the handlers' structure or slow down execution for all other handlers. And so, the solution I settled on was to add to TaskHandlerWithCustomFormatter's initial 'if' statement a simple "or self.prefix_jinja_template is not None", so that it returns if the prefix has already been set. This is similar to what is done by the ElasticSearch handler es_task_handler.py.

Note: also fixed the documentation's example for the handler, as the previous one was incorrect and didn't work.

closes: #35622

---

^ Add meaningful description above Read the Pull Request Guidelines for more information. In case of fundamental code changes, an Airflow Improvement Proposal (AIP) is needed. In case of a new dependency, check compliance with the ASF 3rd Party License Policy. In case of backwards incompatible changes please leave a note in a newsfragment file, named {pr_number}.significant.rst or {issue_number}.significant.rst, in newsfragments.

[boring-cyborg[bot]]

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 Contributors' Guide (https://github.com/apache/airflow/blob/main/contributing-docs/README.rst) Here are some useful points:

• Pay attention to the quality of your code (ruff, 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.
• Always keep your Pull Requests rebased, otherwise your build might fail due to changes not related to your commits. 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

[TiDeane]

Hello, I just rebased my fork, could I get this bug fix merged? @Lee-W

[Lee-W]

Just approved the CI. If everything works fine, I'm planning on merging this early tomorrow. Please let me know if anyone wants to take a deep look

[boring-cyborg[bot]]

Awesome work, congrats on your first merged pull request! You are invited to check our Issue Tracker for additional contributions.