fix(ci): Remove obsolete flagsmith-task-processor clone

[emyller]

Seemingly this outdated configuration has been failing CI for a while.

Changes

• Rely on task_processor package provided by flagsmith-common.

[vercel]

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3 Skipped Deployments

Project	Deployment	Review	Updated (UTC)
docs	Ignored	Preview	Jan 7, 2026 8:33pm
flagsmith-frontend-preview	Ignored	Preview	Jan 7, 2026 8:33pm
flagsmith-frontend-staging	Ignored	Preview	Jan 7, 2026 8:33pm

[github-actions]

Docker builds report

Image	Build Status	Security report
ghcr.io/flagsmith/flagsmith-e2e:pr-6493	Finished ✅	Skipped
ghcr.io/flagsmith/flagsmith-frontend:pr-6493	Finished ✅	Results ✅
ghcr.io/flagsmith/flagsmith-api-test:pr-6493	Finished ✅	Skipped
ghcr.io/flagsmith/flagsmith:pr-6493	Finished ✅	Results ✅
ghcr.io/flagsmith/flagsmith-api:pr-6493	Finished ✅	Results ✅
ghcr.io/flagsmith/flagsmith-private-cloud:pr-6493	Finished ✅	Results ✅

[codecov]

Codecov Report

✅ All modified and coverable lines are covered by tests.
✅ Project coverage is 98.08%. Comparing base (42e4fdc) to head (6fede76).
⚠️ Report is 1 commits behind head on main.

Additional details and impacted files

@@           Coverage Diff           @@
##             main    #6493   +/-   ##
=======================================
  Coverage   98.08%   98.08%           
=======================================
  Files        1296     1296           
  Lines       46616    46616           
=======================================
  Hits        45724    45724           
  Misses        892      892           

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