refactor: use centralized error handling in branch protection controller

[vaaibhavkaushik]

Summary

Refactors the Branch Protection controller to use GitNest's existing centralized error-handling pipeline.

Changes

• Replaced direct inline 500 responses with next(error).
• Converted repository-not-found cases to AppError with status 404.
• Converted repository ownership failures to AppError with status 403.
• Converted branch-protection service validation failures to standardized 422 errors.
• Preserved existing successful response payloads.
• Preserved branch-protection audit event emission.
• Removed duplicated controller-level error-response logic.

Validation

• node --check backend/src/controllers/branchProtection.controller.js
• git diff --check

The full repository test suite currently contains unrelated pre-existing failures involving missing validators, broken exports, rate-limit tests, and other modules outside this PR's scope.

Closes #746

Contributing under GSSoC'26.

[github-actions]

Thank you for your first Pull Request to GitNest! 🚀 We will review your changes soon. Please make sure you've linked the related issues.

[Ankita15k]

@vaaibhavkaushik, please wait until an issue has been assigned to you before opening a PR. Pull requests for unassigned issues will not be considered for review.

Thank you for your understanding and cooperation! 🙌🏻

[vaaibhavkaushik]

@vaaibhavkaushik, please wait until an issue has been assigned to you before opening a PR. Pull requests for unassigned issues will not be considered for review.

Thank you for your understanding and cooperation! 🙌🏻

Thank you for the clarification, @Ankita15k. I understand and apologize for opening the PR before the issue was assigned.

I had already completed the implementation and wanted to contribute, but I'll make sure to wait for an official assignment before opening any future PRs.

If possible, I would be grateful if you could kindly review this PR once, as the changes are already implemented and follow the project's existing patterns. If it cannot be considered due to the repository policy, I completely understand and will follow the assignment process for all future contributions.

Thank you for your time and guidance! 🙏