Keep staging candidate tests on the deployment runner

[anth-volk]

Fixes #3869

Summary

• run the tagged staging candidate integration suite in the deployment job immediately after readiness succeeds
• remove the separate integration job and its additional runner wait
• preserve the existing exact-candidate URL, staging database secret, live simulation checks, and promotion dependencies

Failure reproduced

• https://github.com/PolicyEngine/policyengine-api/actions/runs/37626648234
• the zero-minimum-instance candidate scaled down while integration tests waited for a runner, producing 205-253 second cold starts against a 90-second client timeout

Validation

• actionlint .github/workflows/push.yml
• uv run --frozen pytest tests/unit/test_cloud_run_deploy_scripts.py -q (112 passed)
• uv run --frozen ruff format --check tests/unit/test_cloud_run_deploy_scripts.py
• uv run --frozen ruff check tests/unit/test_cloud_run_deploy_scripts.py
• parsed .github/workflows/push.yml with PyYAML

No environment variables, secrets, service accounts, infrastructure, traffic settings, or API contracts are added or changed.

[codecov]

Codecov Report

✅ All modified and coverable lines are covered by tests.
✅ Project coverage is 87.56%. Comparing base (f03e630) to head (ddedbd0).

Additional details and impacted files

@@             Coverage Diff             @@
##           master    #3870       +/-   ##
===========================================
+ Coverage   45.22%   87.56%   +42.33%     
===========================================
  Files         183      198       +15     
  Lines       11073    12211     +1138     
  Branches     1905     2159      +254     
===========================================
+ Hits         5008    10692     +5684     
+ Misses       5644      922     -4722     
- Partials      421      597      +176     

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