Remove Redis from legacy API test client

[anth-volk]

Fixes #2112

Summary

• replace the legacy rest_client fixture with a Redis-independent api_client fixture
• remove Redis subprocess startup, connection checking, and the fixed startup delay
• update the six affected legacy route-test modules to use the renamed fixture

Testing

• uv run --extra dev ruff check on all changed Python files
• uv run --extra dev pytest on the six affected legacy test modules: 41 passed

[codecov]

Codecov Report

✅ All modified and coverable lines are covered by tests.
✅ Project coverage is 87.18%. Comparing base (5e2071a) to head (ad7d866).
⚠️ Report is 3 commits behind head on master.

Additional details and impacted files

@@             Coverage Diff             @@
##           master    #3815       +/-   ##
===========================================
+ Coverage   46.26%   87.18%   +40.92%     
===========================================
  Files         135      150       +15     
  Lines        7963     8935      +972     
  Branches     1326     1542      +216     
===========================================
+ Hits         3684     7790     +4106     
+ Misses       3990      703     -3287     
- Partials      289      442      +153     

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