[CI] Decouple TPU CI tests to run in parallel with E2E Airflow tests

[RexBearIU]

Description

This PR decouples the TPU unit/integration CI tests from the nightly image build workflow, allowing them to run in parallel with the TPU E2E Airflow tests once the TPU Docker images are pushed.

Specifically:

• Adds a run_tests parameter (default true) to build_and_push_docker_image.yml to control whether unit/integration tests are run inside the build workflow.
• Restructures nightly_images_pipeline.yml to disable nested CI tests during TPU builds (run_tests: false).
• Adds a top-level run_tpu_ci_tests matrix job in nightly_images_pipeline.yml that runs the TPU unit/integration tests concurrently with run_e2e_tests (Airflow E2E tests).
• Keeps GPU CI tests nested inside the GPU build job (default run_tests: true) as GPU does not trigger E2E tests.
• Updates the notify_failure dependencies to monitor all top-level parallel steps.

Tests

• Verified via execution run Run #29006178590, where the TPU CI and E2E Airflow tests triggered and completed in parallel while the GPU nightly builds were still running.

Checklist

• I have performed a self-review of my code. For an optional AI review, add the gemini-review label.
• I have necessary comments in my code, particularly in hard-to-understand areas.
• I have run end-to-end tests tests and provided workload links above if applicable.
• I have made or will make corresponding changes to the doc if needed, including adding new documentation pages to the relevant Table of Contents (toctree directive) as explained in our documentation.

[codecov]

Codecov Report

✅ All modified and coverable lines are covered by tests.

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