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.

tests/test_cli.py

@@ -19,8 +19,24 @@ def test_claude_code_command() -> None:
     command = generate_claude_code_powershell(settings)
 
     assert "ANTHROPIC_BASE_URL" in command
-    assert "claude-sonnet-4.6" in command
-    assert command.endswith("claude")
+    assert "ANTHROPIC_AUTH_TOKEN='dummy'" in command
+    assert "CLAUDE_CODE_ENABLE_GATEWAY_MODEL_DISCOVERY='1'" in command
+    assert "claude-opus-4.6" in command
+    assert command.endswith("claude --model claude-opus-4.6")
+
+
+def test_claude_code_command_uses_custom_model() -> None:
+    settings = Settings.from_values(
+        host="127.0.0.1",
+        port=4141,
+        api_key="test",
+        model="claude-opus-4.6",
+        require_api_key=False,
+    )
+
+    command = generate_claude_code_powershell(settings)
+
+    assert command.endswith("claude --model claude-opus-4.6")
 
 
 def test_missing_api_key_fails(monkeypatch) -> None: