fix(mcp): used logger to log instead of print

Merge https://github.com/google/adk-python/pull/4324

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### Link to Issue or Description of Change

**1. Link to an existing issue (if applicable):**

- Closes: #4320

**2. Or, if no issue exists, describe the change:**

**Problem:**
 Was using print instead of logger for warning message

**Solution:*
Refactored

### Testing Plan

**Unit Tests:**

- [x] I have added or updated unit tests for my change.
- [x] All unit tests pass locally.

_Please include a summary of passed `pytest` results._

**Manual End-to-End (E2E) Tests:**

### Checklist

- [x] I have read the [CONTRIBUTING.md](https://github.com/google/adk-python/blob/main/CONTRIBUTING.md) document.
- [x] I have performed a self-review of my own code.
- [x] I have commented my code, particularly in hard-to-understand areas.
- [x] I have added tests that prove my fix is effective or that my feature works.
- [x] New and existing unit tests pass locally with my changes.
- [x] I have manually tested my changes end-to-end.
- [ ] Any dependent changes have been merged and published in downstream modules.

### Additional context

_Add any other context or screenshots about the feature request here._

COPYBARA_INTEGRATE_REVIEW=https://github.com/google/adk-python/pull/4324 from DineshThumma9:logger_in_mcp_session_clean 5eaa9bdc8c3c6697e75b0e876f043d496dd8ee95
PiperOrigin-RevId: 867601662

src/google/adk/tools/mcp_tool/mcp_session_manager.py

@@ -434,10 +434,9 @@ class MCPSessionManager:
           await exit_stack.aclose()
         except Exception as e:
           # Log the error but don't re-raise to avoid blocking shutdown
-          print(
-              'Warning: Error during MCP session cleanup for'
-              f' {session_key}: {e}',
-              file=self._errlog,
+          logger.warning(
+              f'Error during MCP session cleanup for {session_key}',
+              exc_info=True,
           )
         finally:
           del self._sessions[session_key]

tests/unittests/tools/mcp_tool/test_mcp_session_manager.py

@@ -388,7 +388,8 @@ class TestMCPSessionManager:
     assert len(manager._sessions) == 0
 
   @pytest.mark.asyncio
-  async def test_close_with_errors(self):
+  @patch("google.adk.tools.mcp_tool.mcp_session_manager.logger")
+  async def test_close_with_errors(self, mock_logger):
     """Test cleanup when some sessions fail to close."""
     manager = MCPSessionManager(self.mock_stdio_connection_params)
 
@@ -403,9 +404,6 @@ class TestMCPSessionManager:
     manager._sessions["session1"] = (session1, exit_stack1)
     manager._sessions["session2"] = (session2, exit_stack2)
 
-    custom_errlog = StringIO()
-    manager._errlog = custom_errlog
-
     # Should not raise exception
     await manager.close()
 
@@ -413,10 +411,11 @@ class TestMCPSessionManager:
     exit_stack2.aclose.assert_called_once()
     assert len(manager._sessions) == 0
 
-    # Error should be logged
-    error_output = custom_errlog.getvalue()
-    assert "Warning: Error during MCP session cleanup" in error_output
-    assert "Close error 1" in error_output
+    # Error should be logged via logger.warning
+    mock_logger.warning.assert_called_once()
+    args, kwargs = mock_logger.warning.call_args
+    assert "Error during MCP session cleanup for session1" in args[0]
+    assert kwargs.get("exc_info")
 
   @pytest.mark.asyncio
   @patch("google.adk.tools.mcp_tool.mcp_session_manager.stdio_client")