ci: Upload coverage for private tests, use OIDC

[khvn26]

Thanks for submitting a PR! Please check the boxes below:

• 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

In this PR, we:

1. Run private package tests on both supported Python versions.
2. Upload coverage for private package tests to improve project coverage for PRs.
3. Switch to OIDC-based auth for Codecov.

How did you test this code?

This is a CI change — once CI passes, it's ready to go.

[vercel]

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3 Skipped Deployments

Project	Deployment	Review	Updated (UTC)
docs	Ignored		Jan 26, 2026 9:58am
flagsmith-frontend-preview	Ignored		Jan 26, 2026 9:58am
flagsmith-frontend-staging	Ignored		Jan 26, 2026 9:58am

[github-actions]

Docker builds report

Image	Build Status	Security report
ghcr.io/flagsmith/flagsmith-frontend:pr-6594	Finished ✅	Results ✅
ghcr.io/flagsmith/flagsmith-api-test:pr-6594	Finished ✅	Skipped
ghcr.io/flagsmith/flagsmith-e2e:pr-6594	Finished ✅	Skipped
ghcr.io/flagsmith/flagsmith-api:pr-6594	Finished ✅	Results ✅
ghcr.io/flagsmith/flagsmith-private-cloud:pr-6594	Finished ✅	Results ✅
ghcr.io/flagsmith/flagsmith:pr-6594	Finished ✅	Results ✅

[codecov]

Codecov Report

✅ All modified and coverable lines are covered by tests.
✅ Project coverage is 98.18%. Comparing base (9838589) to head (f588900).
⚠️ Report is 1 commits behind head on main.

Additional details and impacted files

@@            Coverage Diff             @@
##             main    #6594      +/-   ##
==========================================
+ Coverage   98.16%   98.18%   +0.01%     
==========================================
  Files        1295     1295              
  Lines       46793    46920     +127     
==========================================
+ Hits        45934    46067     +133     
+ Misses        859      853       -6     

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