StdioClientTransport#close() does not wait until underlying process is closed #271

Describe the bug

Calling StdioClientTransport#close() does not wait until the underlying process is closed. This makes it hard to properly shut down the server.

To Reproduce

The code snippet in microsoft/playwright-mcp#141 showcases this well. The underlying @playwright/mcp server doesn't exit after calling close(), which is a bug in the implementation, but it can't be observed from the code because StdioClientTransport#close() returns immediately.

Expected behavior

close() blocks until the underlying process exits.

Additional context

close() returns a Promise, which implies that it waits for something.