Logging & Observability Correctness

Enforce correct logging and error handling patterns in the sentry-mcp codebase. The core principle: 4xx errors (user-correctable) must NEVER create Sentry issues. 5xx errors (system failures) must ALWAYS create Sentry issues.

Error Hierarchy

API Errors (packages/mcp-core/src/api-client/errors.ts)

ApiError (base class)
├─ ApiClientError (4xx - user errors, NOT sent to Sentry)
│  ├─ ApiPermissionError (403)
│  ├─ ApiNotFoundError (404)
│  ├─ ApiValidationError (400, 422)
│  ├─ ApiAuthenticationError (401)
│  └─ ApiRateLimitError (429)
└─ ApiServerError (5xx - system errors, SENT to Sentry)