ci: use gh cli in ci-router to dispatch worker/api/shared jobs

[matt-codecov]

two things:

• as-is, we are limited to 20 nested workflow calls shared between ci-router.yml, worker-ci.yml, api-ci.yml, and shared-ci.yml. i think by using the gh cli to invoke worker/api/shared CI, we sidestep that limit and api/shared/worker each get their own limit of 20 to work with.
• push-stage.yml is also moved back inside worker-ci.yml and api-ci.yml. any push to staging should now result in a deploy of that commit for both worker and api.

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[seer-by-sentry]

Sentry detected 1 potential issue in your recent changes

Suspicion of a critical bug: The new `gh workflow run` commands lack error handling, causing the CI pipeline to fail unexpectedly on transient issues like API errors, potentially blocking deployments.

• Description: The analysis indicates that the gh workflow run commands used to dispatch sub-workflows lack explicit error handling. Due to the default set -e behavior in GitHub Actions bash shells, any non-zero exit code from these commands will immediately fail the step and the entire job. This means that transient issues, such as GitHub API rate limits, network problems, or GitHub CLI panics, which are realistic operational concerns, will cause the CI router workflow to fail unexpectedly. This failure blocks the entire CI pipeline, preventing subsequent steps like PR merges and deployments, effectively crashing the build process for that commit. The specific code paths affected are the steps executing gh workflow run for api-ci.yml, worker-ci.yml, and shared-ci.yml. For instance, if the GitHub API returns a rate limit error (resulting in a non-zero exit code) when attempting to dispatch api-ci.yml, the dispatch-api-ci job will fail immediately. This represents a reduction in robustness compared to the previous workflow_call approach, which had built-in retry/error handling mechanisms.
• Code location: .github/workflows/ci-router.yml:86~93
• Suggested fix: Add error handling to the gh workflow run commands, such as using || true or implementing retry logic, to prevent transient failures from crashing the entire CI workflow.

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[codecov-notifications]

Codecov Report

All modified and coverable lines are covered by tests ✅

✅ All tests successful. No failed tests found.

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[codecov]

Codecov Report

All modified and coverable lines are covered by tests ✅

Project coverage is 94.20%. Comparing base (f700797) to head (52adf08).
Report is 2 commits behind head on main.

✅ All tests successful. No failed tests found.

Additional details and impacted files

@@           Coverage Diff           @@
##             main     #234   +/-   ##
=======================================
  Coverage   94.20%   94.20%           
=======================================
  Files        1214     1214           
  Lines       45036    45036           
  Branches     1434     1434           
=======================================
  Hits        42424    42424           
  Misses       2309     2309           
  Partials      303      303           

Flag	Coverage Δ
apiunit	96.46% <ø> (ø)
sharedintegration	39.73% <ø> (ø)
sharedunit	88.11% <ø> (ø)
workerintegration	61.61% <ø> (ø)
workerunit	90.62% <ø> (ø)

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[codspeed-hq]

CodSpeed Performance Report

Merging #234 will not alter performance

_{Comparing matt/ci-refactor (52adf08) with main (ea75610)}

Summary

✅ 9 untouched benchmarks