Enhance README with post-installation checklist and real-world use cases

[RellikSai]

This PR adds two sections to the Apache Airflow README:

1. Post-Installation Checklist: A guide to help users verify their Airflow installation.
2. Airflow in Practice: Examples of 5 real-world use cases to showcase how Airflow is used in production environments.

These additions will help new users validate their installation and understand practical use cases of Airflow.

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Was generative AI tooling used to co-author this PR?

• Yes (please specify the tool below)

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• Read the Pull Request Guidelines for more information. Note: commit author/co-author name and email in commits become permanently public when merged.
• For fundamental code changes, an Airflow Improvement Proposal (AIP) is needed.
• When adding dependency, check compliance with the ASF 3rd Party License Policy.
• For significant user-facing changes create newsfragment: {pr_number}.significant.rst or {issue_number}.significant.rst, in airflow-core/newsfragments.

[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 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 prek-hooks 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: dev@airflow.apache.org
  Slack: https://s.apache.org/airflow-slack

[RellikSai]

Hello,

This is a comment regarding this pull request, which has been open for about a week. I have recently updated the branch with the latest changes from main, and it should now be up to date.

Please let me know if any changes or improvements are required from my side to move this PR forward. I would be happy to address them.

Thank you very much for your time and consideration.