Python-based server restarts

Bug description

Python-based MCP servers crash when a second client connects through ToolHive's stdio proxy. The proxy forwards a second initialize request to an already-initialized session, causing a Pydantic validation error that crashes the Python process.

Steps to reproduce

1. Deploy a Python MCP server via ToolHive with stdio transport: thv run docker.io/mcp/git:latest --name git --transport stdio --proxy-mode streamable-http
2. Connect a first MCP client - works fine
3. Connect a second MCP client or wait several minutes for ToolHive's internal health check
4. Container crashes with exit code 1

Expected behavior

The proxy should handle multiple client connections by either:

• Multiplexing clients onto the single stdio session without re-sending initialize
• Resetting the session before forwarding a new initialize

Actual behavior

The proxy forwards the second initialize request to the active stdio session. The Python MCP SDK's _receive_loop tries to validate it as a ClientRequest (which only accepts post-initialization requests like ping, tools/call, etc.), fails with validation errors, and crashes:

pydantic_core.ValidationError: 20 validation errors for ClientRequest
InitializeRequest.params                                                
  Field required [type=missing, input_value={'method': 'initialize', ...

Node.js MCP servers, for example, don't crash on unexpected messages, so they're unaffected.

Environment

• ToolHive v0.9.3
• Podman
• MacOS

Start by tracing ToolHive's stdio proxy handling for initialize messages and reproduce the failure with the provided thv run command. Done means a second client connection or internal health check no longer forwards an invalid second initialize request, and the Python MCP server remains running.