ci: Migrate api/ from Poetry to uv

[khvn26]

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• I have read the Contributing Guide.
• I have added information to docs/ if required so people know about the feature.
• I have filled in the "Changes" section below.
• I have filled in the "How did you test this code" section below.

Changes

Migrates the API project from Poetry to uv for dependency management:

• api/pyproject.toml: Converted from Poetry to PEP 440/735 format with setuptools build backend and auto-discovery
• api/Makefile: Replaced poetry run with uv run, updated install targets
• Dockerfile: Updated for uv environment variables (UV_PROJECT_ENVIRONMENT, UV_COMPILE_BYTECODE, UV_LINK_MODE) and --group syntax
• GitHub workflows: Use astral-sh/setup-uv action instead of Poetry
• .pre-commit-config.yaml: Updated hooks for uv, replaced poetry-check with uv-lock-check
• api/.gitignore: Added *.egg-info/
• Consolidated private dependency groups (auth-controller, saml, ldap, workflows, licensing, release-pipelines) into single private group

How did you test this code?

• Ran make install locally - completed successfully
• Ran make test locally - 2888 passed, 38 skipped
• Verified uv lock generates valid lockfile
• Verified dependency parsing in Makefile works correctly

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3 Skipped Deployments

Project	Deployment	Review	Updated (UTC)
docs	Ignored		Jan 17, 2026 4:40am
flagsmith-frontend-preview	Ignored		Jan 17, 2026 4:40am
flagsmith-frontend-staging	Ignored		Jan 17, 2026 4:40am

[codecov]

Codecov Report

✅ All modified and coverable lines are covered by tests.
✅ Project coverage is 98.09%. Comparing base (c1ffe45) to head (7c4f4db).

Additional details and impacted files

@@            Coverage Diff             @@
##             main    #6546      +/-   ##
==========================================
- Coverage   98.09%   98.09%   -0.01%     
==========================================
  Files        1293     1293              
  Lines       46587    46587              
==========================================
- Hits        45699    45698       -1     
- Misses        888      889       +1     

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