Fix GitHub OAuth sign-in redirect

[398724221]

Summary

• Fixes 🏭 Bounty T1: Fix GitHub OAuth Sign-In Flow #821
• Centralizes GitHub sign-in redirects through one OAuth helper
• Falls back to the official GitHub authorize URL when /api/auth/github/authorize is unavailable, instead of redirecting users to a 404-prone relative API route
• Adds client-side OAuth state generation/storage and callback state validation before exchanging the code
• Replaces remaining hard-coded /api/auth/github/authorize sign-in entry points
• Adds missing shared frontend utility modules required for the production build

Verification

• npm test -- auth.test.ts --run
• npm run build
• git diff --check

Notes

• npm test -- --run still fails on existing baseline issues unrelated to this PR: missing Playwright dependency for frontend/tests/e2e/* and many existing tests importing components/modules that are not present in the repo. The focused OAuth tests and production build pass.

Bounty

Submitting for the T1 bounty in #821. Payout details can be coordinated after review/merge.