Stabilize live integration tests

[anth-volk]

Fixes #3555

Summary

• add a per-run suffix to integration_probe_id so workflow reruns do not reuse stale staging cache keys
• centralize live endpoint polling and retry transient request errors plus HTTP 5xx responses until the integration deadline
• reduce live calculate smoke payload axis count from 401 to 101
• keep both national and Utah economy live tests while avoiding exact-value assertions that drift with model/data updates
• remove the live budget-window in-flight dedupe assertion and rely on the non-live integration test for that behavior

Related Failure

• https://github.com/PolicyEngine/policyengine-api/actions/runs/25396143607/job/74488516912

Testing

• ruff check tests/integration/conftest.py tests/integration/test_live_economy.py tests/integration/test_live_budget_window_cache.py tests/integration/test_budget_window_in_flight_dedupe.py
• ruff format --check tests/integration/conftest.py tests/integration/test_live_economy.py tests/integration/test_live_budget_window_cache.py tests/integration/test_budget_window_in_flight_dedupe.py
• .venv/bin/python -m pytest tests/integration/test_budget_window_in_flight_dedupe.py -q
• .venv/bin/python -m pytest tests/integration/test_live_calculate.py tests/integration/test_live_economy.py tests/integration/test_live_budget_window_cache.py --collect-only -q

[codecov]

Codecov Report

✅ All modified and coverable lines are covered by tests.
✅ Project coverage is 78.94%. Comparing base (0d99785) to head (5f71127).
⚠️ Report is 2 commits behind head on master.

Additional details and impacted files

@@           Coverage Diff           @@
##           master    #3556   +/-   ##
=======================================
  Coverage   78.94%   78.94%           
=======================================
  Files          65       65           
  Lines        3762     3762           
  Branches      662      662           
=======================================
  Hits         2970     2970           
  Misses        614      614           
  Partials      178      178           

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