[SPARK-49142][FOLLOWUP][CONNECT][PYTHON] Use PySparkLogger for Spark …

…Connect client log

### What changes were proposed in this pull request?

This followups for #47647 to switch the standard logger into PySparkLogger for Spark Connect client log

### Why are the changes needed?

Use PySpark specific logger

### Does this PR introduce _any_ user-facing change?

No

### How was this patch tested?
CI

### Was this patch authored or co-authored using generative AI tooling?

No

Closes #47822 from itholic/update_pyspark_logger.

Authored-by: Haejoon Lee <haejoon.lee@databricks.com>
Signed-off-by: Hyukjin Kwon <gurwls223@apache.org>

python/pyspark/sql/connect/client/logging.py

@@ -17,6 +17,7 @@
 
 
 import logging
+from pyspark.logger import PySparkLogger
 import os
 from typing import Optional
 
@@ -27,7 +28,7 @@
 
 def _configure_logging() -> logging.Logger:
     """Configure logging for the Spark Connect clients."""
-    logger = logging.getLogger(__name__)
+    logger = PySparkLogger.getLogger(__name__)
     handler = logging.StreamHandler()
     handler.setFormatter(
         logging.Formatter(fmt="%(asctime)s %(process)d %(levelname)s %(funcName)s %(message)s")