[AIRFLOW-5402] Remove deprecated logger

[Fokko]

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Removing the deprecated logger for Airflow 2.0

Jira

• My PR addresses the following Airflow Jira issues and references them in the PR title. For example, "[AIRFLOW-5402] My Airflow PR"
  • https://issues.apache.org/jira/browse/AIRFLOW-5402
  • In case you are fixing a typo in the documentation you can prepend your commit with [AIRFLOW-XXX], code changes always need a Jira issue.
  • In case you are proposing a fundamental code change, you need to create an Airflow Improvement Proposal (AIP).
  • In case you are adding a dependency, check if the license complies with the ASF 3rd Party License Policy.

Description

• Here are some details about my PR, including screenshots of any UI changes:

Tests

• My PR adds the following unit tests OR does not need testing for this extremely good reason:

Commits

• My commits all reference Jira issues in their subject lines, and I have squashed multiple commits if they address the same issue. In addition, my commits follow the guidelines from "How to write a good git commit message":
  1. Subject is separated from body by a blank line
  2. Subject is limited to 50 characters (not including Jira issue reference)
  3. Subject does not end with a period
  4. Subject uses the imperative mood ("add", not "adding")
  5. Body wraps at 72 characters
  6. Body explains "what" and "why", not "how"

Documentation

• In case of new functionality, my PR adds documentation that describes how to use it.
  • All the public functions and the classes in the PR contain docstrings that explain what it does
  • If you implement backwards incompatible changes, please leave a note in the Updating.md so we can assign it to a appropriate release