Error responses are inconsistent between REST, validation, and exception filters

[nanaf6203-bit]

Context

ResponseFormatInterceptor standardizes success payloads; ValidationExceptionFilter/PrismaExceptionFilter/AllExceptionsFilter emit { statusCode, message, ... } shapes with overlapping fields; DTOs throw BadRequestException at various shapes too.

Problem

Clients observe inconsistent error envelopes per module (array vs string message, presence of path/timestamp), making API SDKs fragile; docs API_VERSIONING doesn't specify the error contract.

Proposed approach

Define a single ErrorResponse contract (code, message, details, traceId - trace interceptor already sets x-trace-id), align the three filters + ValidationPipe exceptionFactory, and add an e2e that snapshots error shapes across representative routes.

Acceptance criteria

• All error responses share the documented envelope; snapshot test enforces it.