feat: Comprehensive server health check with 3-step diagnostics

Replace single TCP self-test with three distinct checks:
1. Unity TCP Server - is the internal TCP listener running?
2. MCP Server Connected - is a Python MCP server connected as client?
3. uvx Command - can the configured uvx executable be found and run?

Each check shows its own status dot (green/red/orange) and detail text.
The uvx check runs `uvx --version` (or custom path) to verify availability.

Co-Authored-By: Claude Opus 4.6 <noreply@anthropic.com>