UI E2E Test || DAGRUNS-001: Verify all DAG runs display

[vatsrahul1001]

Description

Add an E2E test to verify the DAG Runs page (/dag_runs) displays all DAG runs correctly.

What to test

• Navigate to the DAG Runs page
• Verify the DAG runs table renders
• Verify run details display: DAG ID, run ID, state, start time, end time
• Verify different run states are visually distinct (success, failed, running)
• Verify Fitering works
• Verify Pagination works

Related issues

#59028

Are you willing to submit a PR?

• Yes I am willing to submit a PR!

Code of Conduct

• I agree to follow this project's Code of Conduct

[lin121291]

Hi! I'd like to work on this issue. I have backend engineering experience. Please let me know if there are any code sections, expectations, or patterns I should follow.
Thanks!

[vatsrahul1001]

@lin121291 refer to below information which will be helpful, you can reach out in case of any question and doubt on slack channel #sig-airflow-ui-e2e-tests

What's Been Merged:

Playwright framework with TypeScript (##58548 )
CI workflow integrated (#58901)
Initial test covering login and DAG triggering
Contribution Guide
https://github.com/apache/airflow/blob/main/airflow-core/src/airflow/ui/tests/e2e/README.md#contributing-new-tests