[EM] Improve MCP readiness during gateway startup

[astandrik]

Goal

Make MCP readiness explicit and ensure startup recovers promptly when its dependencies become available.

Work

• Review ordering between Gateway startup and MCP tool initialization.
• Keep service liveness and MCP readiness distinct.
• Cover delayed dependencies and recovery with bounded retries where needed.

Done when

• Tests cover normal startup, delayed dependencies and unavailable dependencies.
• MCP is reported ready only when initialization and tools/list work.
• Recovery has documented timing and does not use unbounded retries.
• The supported client can reconnect after a service restart.

Tracked in the UI backlog; implementation belongs to the native EM backend. Deployment is separate.