Unity AI MCP connection resets when multiple Unity instances are opened

How to reproduce:

1. Create 2 new projects
2. Open the 2 instances of the Unity Editor
3. Enable Unity MCP in both Editors
4. Using Claude Code desktop, connect to the Unity instances
5. Observe the connections in Claude Code desktop

Actual result: Connection switches randomly between clients and sessions do not expire
Expected result: Connection is stable and sessions expire

Reproducible with: 1.0.0-pre.2 (6000.3.17f1), 2.11.0-pre.1 (6000.3.17f1)

Reproducible on: Windows 11 x64
Not reproducible on: No other environments tested