feat: Implement centralized backend error handling

[ApostolisFalaras]

Description

Implement consistent error handling for API validation, DBMS errors, process failures, and unexpected backend failures.

Tasks

• Add centralized Express error middleware
• Define backend error response format
• Map invalid requests to client errors
• Map missing resources to not-found errors
• Map DBMS query errors
• Map DBMS process failures
• Hide internal stack traces from API responses
• Log unexpected backend errors

Acceptance Criteria

• API errors use a consistent JSON structure.
• DBMS errors are readable by the frontend.
• Internal implementation details are not exposed.
• Unexpected errors do not terminate the server.

Depends On

• feat: Initialize Node.js backend server