Fix Windows: Use taskkill /T directly without graceful termination

On Windows, process.terminate() only kills the parent process, not
children. By the time we timeout and call taskkill /T, the parent
is already dead and child processes might not be properly associated.

Instead, directly use taskkill /T on Windows to kill the entire
process tree in one operation. This matches what the debug scripts
showed - taskkill /T works when called directly on a live parent.

Author: felixweinberger

src/mcp/client/stdio/__init__.py

@@ -326,14 +326,6 @@ async def _terminate_process_with_children(process: Process | FallbackProcess, t
         if not pid:
             return
 
-        # Try graceful termination first
-        try:
-            process.terminate()
-            with anyio.fail_after(timeout):
-                await process.wait()
-        except TimeoutError:
-            # On Windows, we need to recursively kill all child processes
-            # because taskkill /T doesn't always work with Python subprocesses
-            await _kill_process_tree_windows(pid)
-        except ProcessLookupError:
-            pass
+        # On Windows, directly use taskkill /T to kill the entire process tree
+        # Don't try graceful termination first as it only kills the parent
+        await _kill_process_tree_windows(pid)