feat: add centralized error handling with error codes and validation …

[Tobi-8]

Closes #107

What

Adds a centralized error handling module with custom exception classes, error codes, and field-level validation error responses.

Changes

• src/common/errors/error-codes.ts — ErrorCode enum for consistent programmatic error identification (NOT_FOUND, UNAUTHORIZED, VALIDATION_ERROR, CONFLICT, etc.)
• src/common/errors/app.exception.ts — Base AppException class extending HttpException with an errorCode field, plus convenience subclasses: NotFoundException, UnauthorizedException, ForbiddenException, BadRequestException, ConflictException, RateLimitException
• src/common/filters/global-exception.filter.ts — Updated to:
  • Include errorCode in all error responses
  • Extract and return field-level validation errors for 400 responses (class-validator)
  • Reuse x-request-id header as correlation ID when present
  • Extract Sentry reporting and logging into helper methods
• src/common/index.ts — Re-exports new exception classes and error codes

Error Response Format

All errors now return:

{
  "statusCode": 400,
  "errorCode": "VALIDATION_ERROR",
  "message": "Validation failed",
  "errors": { "email": ["email must be an email"] },
  "correlationId": "...",
  "timestamp": "2026-07-21T...",
  "path": "/api/v1/auth/register"
}
Validation errors, 401, 403, 404, and 409 all map to their correct HTTP status codes with matching errorCode values. Stack traces remain hidden in production, visible in development.
Why
Standardizes error responses across the API so clients can handle errors programmatically using errorCode instead of parsing message strings. Existing services using NestJS built-in exceptions continue to work unchanged — the filter maps their status codes to error codes automatically.

closes #107