[Bug]: Session invalidated after Unity-MCP server restarts, requiring full client restart

[whatevertogo]

Description
When the unity-mcp server is restarted, any active sessions in the client (Claude Code / Codex) become immediately invalid. The client does not seem to handle session recovery or re-authentication automatically.

Current Behavior
Start unity-mcp server.

Authenticate and connect via Claude Code or Codex.

Restart the unity-mcp server.

The client fails to communicate with the server (Session ID invalid/expired).

Current Workaround: I must completely restart Claude Code/Codex. If using the VS Code extension, I have to restart the entire VS Code window to restore the connection.

I used localHTTP and had a VPN enabled, which might also have caused an impact.

Additionally, starting a second Claude Code client instance immediately invalidates the session of the first active client.