[Task]: Add CI format check on pull requests

[dellch]

Description

Add a GitHub Actions workflow that runs on pull requests and verifies formatting has been applied. The workflow should:

• Run dotnet format --verify-no-changes for backend code
• Run npx prettier --check (or equivalent) for frontend code
• Fail the PR if either check reports unformatted files

This enforces the make format convention at the CI level so unformatted code can't be merged.

Dependencies

Depends on #3 (frontend scaffold) being merged so the frontend tooling is available.