refactor(mcp): modularize MCP and tray menu logic
Split mcp.rs (1135 lines) into focused modules:
- validation.rs: server config validation
- claude.rs: Claude MCP sync/import
- codex.rs: Codex MCP sync (TOML handling)
- gemini.rs: Gemini MCP sync/import
Extract tray menu logic from lib.rs to tray.rs for better separation of concerns.