Revert FallbackProcess to synchronous termination approach

This reverts the FallbackProcess termination logic to use synchronous
wait in a thread rather than async polling. The previous async polling
approach with anyio.sleep(0.1) may have been causing resource cleanup
issues in Windows CI with Python 3.10.

The synchronous approach:
- Uses to_thread.run_sync() to wait for process termination
- Removes the timeout-based termination attempt
- Simplifies the wait() method to directly use popen.wait()

This should resolve the unclosed transport warnings seen in CI tests.

Author: felixweinberger

src/mcp/client/stdio/win32.py

@@ -8,7 +8,7 @@
 from pathlib import Path
 from typing import BinaryIO, TextIO, cast
 
-import anyio
+from anyio import to_thread
 from anyio.abc import Process
 from anyio.streams.file import FileReadStream, FileWriteStream
 
@@ -74,18 +74,9 @@ async def __aexit__(
         exc_val: BaseException | None,
         exc_tb: object | None,
     ) -> None:
-        """Clean up process and streams.
-
-        Attempts to terminate the process, but doesn't fail if termination
-        is not possible (e.g., process already dead or being handled elsewhere).
-        """
-        try:
-            self.popen.terminate()
-            with anyio.move_on_after(0.5):
-                await self.wait()
-        except (ProcessLookupError, OSError):
-            # Process already dead or being handled elsewhere
-            pass
+        """Terminate and wait on process exit inside a thread."""
+        self.popen.terminate()
+        await to_thread.run_sync(self.popen.wait)
 
         # Close the file handles to prevent ResourceWarning
         if self.stdin:
@@ -100,13 +91,8 @@ async def __aexit__(
             self.stderr.close()
 
     async def wait(self):
-        """
-        Poll the process status instead of blocking wait
-        This allows anyio timeouts to work properly
-        """
-        while self.popen.poll() is None:
-            await anyio.sleep(0.1)
-        return self.popen.returncode
+        """Async wait for process completion."""
+        return await to_thread.run_sync(self.popen.wait)
 
     def terminate(self):
         """Terminate the subprocess immediately."""