Refactor models and logging for nexus-claude-api

- Update default models in config to use `claude-opus-4.6`.
- Introduce logging configuration to write logs to a file.
- Add correlation ID to error responses for better traceability.
- Implement diagnostics for summarizing message requests.
- Normalize legacy system messages in the API.
- Enhance tests to cover new logging and error handling features.
- Update README and documentation to reflect changes in model defaults and logging behavior.

src/nexus_claude_api/server.py

@@ -1,7 +1,5 @@
 from __future__ import annotations
 
-import logging
-
 from fastapi import FastAPI
 from fastapi.middleware.cors import CORSMiddleware
 from fastapi.requests import Request
@@ -44,9 +42,4 @@ def create_app(
             error_type=exc.error_type,
         )
 
-    logging.basicConfig(
-        level=logging.DEBUG if resolved_settings.verbose else logging.INFO,
-        format="%(asctime)s %(levelname)s %(name)s: %(message)s",
-    )
     return app
-