CI: Run CI tests on stable deps in Docker image pipelines and explicitly name test jobs

[SurbhiJainUSC]

Description

This PR updates the nightly Docker image workflows to run CI tests on stable dependencies, relocates the Docker image promotion step, expands the CPU test suite, and improves the GitHub Actions UI by explicitly naming test jobs.

Specifically, this change:

• Refactors test execution: Removes the run_tests input and the integrated run_ci_tests job from the shared .github/workflows/build_and_push_docker_image.yml workflow. Test execution is now explicitly handled by caller workflows.
• Updates GPU & TPU pipelines:
  • Adds a new run_ci_tests job to .github/workflows/gpu_nightly_images_pipeline.yml to run Pre-Training CI tests against the maxtext_gpu_jax_stable image.
  • Simplifies the test matrix in .github/workflows/tpu_nightly_images_pipeline.yml by testing on maxtext_jax_stable (Pre-Training) and maxtext_post_training_nightly (Post-Training).
• Relocates image tagging: Moves the tag_docker_image job out of the TPU nightly pipeline and directly into .github/workflows/run_ci_tests.yml. This ensures that images are only tagged as verified-${GITHUB_RUN_ID} and latest if they successfully pass the test suite.
• Expands CPU testing: Adds cpu-integration tests to .github/workflows/run_tests_coordinator.yml and .github/workflows/ci_pipeline.yml.
• Improves GitHub Actions UI: Adds explicit name: attributes to jobs across multiple workflows (e.g., build_package.yml, ci_pipeline.yml, check_docs_build.yml, docs_link_check.yml, etc.) to make the pipeline UI easier to read.

Tests

TPU nightly Docker image pipeline: https://github.com/AI-Hypercomputer/maxtext/actions/runs/31567082881

Checklist

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• 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.

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[codecov]

Codecov Report

✅ All modified and coverable lines are covered by tests.

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