fix: eliminate JSON logging duplication in litellm-proxy-extras

- Integrate litellm_proxy_extras logger with global JSON logging setting
- Prevent log propagation to avoid duplicate text/JSON output
- Use consistent JSON format when json_logs is enabled
- Simplify logging implementation for maintainability

Fixes issue where proxy startup logs appeared twice (text + JSON)
when json_logs: true was configured.

litellm-proxy-extras/litellm_proxy_extras/_logging.py

@@ -1,12 +1,42 @@
+import json
 import logging
+import os
+from datetime import datetime
+
+
+class JsonFormatter(logging.Formatter):
+    def formatTime(self, record, datefmt=None):
+        dt = datetime.fromtimestamp(record.created)
+        return dt.isoformat()
+
+    def format(self, record):
+        json_record = {
+            "message": record.getMessage(),
+            "level": record.levelname,
+            "timestamp": self.formatTime(record),
+        }
+        if record.exc_info:
+            json_record["stacktrace"] = self.formatException(record.exc_info)
+        return json.dumps(json_record)
+
+
+def _is_json_enabled():
+    try:
+        import litellm
+        return getattr(litellm, 'json_logs', False)
+    except (ImportError, AttributeError):
+        return os.getenv("JSON_LOGS", "false").lower() == "true"
+
 
-# Set up package logger
 logger = logging.getLogger("litellm_proxy_extras")
-if not logger.handlers:  # Only add handler if none exists
+
+if not logger.handlers:
     handler = logging.StreamHandler()
-    formatter = logging.Formatter(
-        "%(asctime)s - %(name)s - %(levelname)s - %(message)s"
-    )
-    handler.setFormatter(formatter)
+    if _is_json_enabled():
+        handler.setFormatter(JsonFormatter())
+    else:
+        handler.setFormatter(logging.Formatter("%(asctime)s - %(name)s - %(levelname)s - %(message)s"))
     logger.addHandler(handler)
     logger.setLevel(logging.INFO)
+
+logger.propagate = False