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/logging_config.py

@@ -0,0 +1,26 @@
+from __future__ import annotations
+
+import logging
+from pathlib import Path
+
+
+LOG_DIR = Path("logs")
+LOG_FILE = LOG_DIR / "nexus-claude-api.log"
+LOG_FORMAT = "%(asctime)s %(levelname)s %(name)s: %(message)s"
+
+
+def configure_logging(*, verbose: bool = False, log_file: Path = LOG_FILE) -> Path:
+    log_file.parent.mkdir(parents=True, exist_ok=True)
+
+    formatter = logging.Formatter(LOG_FORMAT)
+    file_handler = logging.FileHandler(log_file, encoding="utf-8")
+    file_handler.setLevel(logging.DEBUG)
+    file_handler.setFormatter(formatter)
+
+    app_logger = logging.getLogger("nexus_claude_api")
+    app_logger.handlers.clear()
+    app_logger.setLevel(logging.DEBUG if verbose else logging.INFO)
+    app_logger.addHandler(file_handler)
+    app_logger.propagate = False
+
+    return log_file