Add testing with Real MCP Client

### Describe the Request

The testing with the python_sdk left lots of bugs and errors. (See #3).  We need to figure out if there is a way to set up tests using a real MCP client, because there seem to be issues that can't be found with the python_sdk.

Maybe there is a way to replay requests from Claude?

### Sample Code

```python

```

### Additional Code or Information

```console

```