fix: normalize room github usernames

[nyxsky404]

Summary

Normalized collaboration room membership to use stable GitHub logins and case-insensitive invite checks.

Closes #2183

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Type of Change

• Bug fix
• New feature
• Documentation update
• Refactor / code cleanup

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Changes Made

• Updated room API routes to use session.githubLogin instead of session.user.name
• Added shared room username helpers for validation and case-insensitive comparison
• Normalized invited usernames before GitHub lookup and storage
• Stored the canonical login returned by the GitHub API when inviting members
• Added focused tests for username normalization and mixed-case comparison

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How to Test

Steps for the reviewer to verify this works:

1. Run npm run test -- rooms.test.ts
2. Create or access a collaboration room with an authenticated GitHub account
3. Invite a user with mixed casing, such as Octocat
4. Attempt to invite the same user again with different casing, such as octocat
5. Verify the second invite is rejected as an existing member

Validation performed:

• npm run test -- rooms.test.ts passes
• npm run type-check currently fails on existing project-wide dependency/type issues unrelated to this change
• npm run lint currently fails before linting because @ducanh2912/next-pwa is missing from local module resolution

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Screenshots (if UI change)

N/A

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Checklist

• Linked issue in summary
• npm run lint passes locally
• No TypeScript errors (npm run type-check)
• Self-reviewed the diff
• Added/updated tests if applicable

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Accessibility Checklist

• Proper keyboard navigation tested
• Responsive UI verified
• Accessibility labels added where needed

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Additional Notes

This change intentionally avoids a database migration and fixes the behavior at the API layer. A future migration could add a case-insensitive uniqueness constraint for stronger database-level enforcement.

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[github-actions]

GSSoC Label Checklist 🏷️

@Priyanshu-byte-coder — please apply the appropriate labels before merging:

Difficulty (pick one):

• level:beginner — 20 pts
• level:intermediate — 35 pts
• level:advanced — 55 pts
• level:critical — 80 pts

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• quality:clean — ×1.2 multiplier
• quality:exceptional — ×1.5 multiplier

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Type labels (type:*) are auto-detected from files and title. Review and adjust if needed.
Points formula: (difficulty × quality_multiplier) + type_bonus

[Priyanshu-byte-coder]

This PR now has a merge conflict with main after the Supabase client security split in #2114 was merged (which also modified the rooms routes).

Please rebase your branch on main to resolve the conflicts:

git fetch origin
git rebase origin/main

Once the conflicts are resolved and CI passes, we can merge this.

[nyxsky404]

@Priyanshu-byte-coder The 11 failing Playwright smoke tests are pre-existing failures unrelated to this PR's changes. The failures are in api.spec.ts, dashboard.spec.ts, goals.spec.ts, and streak.spec.ts - none of which touch the rooms code changed here.