fix: use factory to refresh session once it is finished

[arnewouters]

Summary

Changes

Please provide a summary of what's being changed

Timeouts stop the background session task in FastMCP, this makes follow-up tool calls fail with

MCP Tool Error Response: Internal error: nesting counter should be 0 when starting new session, got 2

With this PR, we are explicitly refreshing the session when the client is no longer connected.

User experience

Please share what the user experience looks like before and after this change

config for testing:

    "example-mcp-server": {
      "command": "uv",
        "args": [
          "run",
          "--directory",
          "/Volumes/workplace/mcp-proxy-for-aws-dev",
          "mcp-proxy-for-aws",
          "--service",
          "my-service",
          "--region",
          "us-east-1",
          "--log-level",
          "DEBUG",
          "https://example.com/mcp"
        ],
        "env": {},
        "disabled": false,
        "autoApprove": []
    }

Cline

Before:

There is an error after a timeout

After:

Session refreshes under the hood and the next call succeeds

Checklist

If your change doesn't seem to apply, please leave them unchecked.

• I have reviewed the contributing guidelines
• I have performed a self-review of this change
• Changes have been tested
• Changes are documented

Is this a breaking change? (Y/N)

• Yes
• No

Please add details about how this change was tested.

• Did integration tests succeed?
• If the feature is a new use case, is it necessary to add a new integration test case?

Acknowledgment

By submitting this pull request, I confirm that you can use, modify, copy, and redistribute this contribution, under the terms of your choice.

[wzxxing]

The client should be a ProxyClient.

[arnewouters]

Why? We are doing the same as FastMCP.as_proxy https://github.com/jlowin/fastmcp/blob/ba69fba3055db6938ba368dc17275a85ca626ae3/src/fastmcp/server/server.py#L2612-L2634

[wzxxing]

Because we probably want a mix of the if-else branches

1. connect the session to be reused
2. use ProxyClient to support features like elicitation and sampling; the regular client does not support

[wzxxing]

what if you do client.new() here?

[arnewouters]

It returns Client and not ProxyClient

[wzxxing]

When this method throws, the client also hangs, the _initialize_client context manager writes the jsonrpc error to stdout.

Can this be done here too? I think it is a bit tricky to get the new json rpc message id.