feat: standardize backend error responses and improve error handling

[Ni-zav]

Description

This PR standardizes backend API error responses to match the documented format and improves error handling throughout the FastAPI backend.

Related Issue

[Link to the issue this PR addresses (e.g., "Fixes #123")]

Type of Change

• Bug fix
• New feature
• Documentation update
• Performance improvement
• Code refactoring
• Other (please describe)

Testing

• Unit tests added/updated
• Manual testing performed
• All tests pass

Documentation

• Documentation updated
• No documentation needed

Checklist

• Code follows project style
• Self-reviewed the code
• Added comments for complex code
• Updated README if needed
• Branch is up to date with devtest
• No merge conflicts

Screenshots (if applicable)

[Add screenshots here if your changes affect the UI]

Additional Notes

• Used start_python_backend.cmd
• Tested endpoints with valid and invalid requests using PowerShell
• Confirmed error responses for known endpoints match the documented format
• Verified that default FastAPI 404/422 errors for unknown routes or validation still use FastAPI’s format (expected)