Feature: Implement WebSockets or SSE for Real-Time UI Updates

[hypnoastic]

Description

The monitoring dashboard currently relies on short-polling (fetching /api/state every few seconds) to keep the frontend updated. This can cause unnecessary network overhead and minor stuttering/lag during active executions.

Proposal

Implement WebSockets or Server-Sent Events (SSE) to push state updates directly from the backend to the frontend exactly when changes occur.

Acceptance Criteria

• Refactor the backend to support WS/SSE connections.
• Update the frontend Javascript to listen for pushed events rather than polling.
• Ensure UI components (Runs, Agents, Playground) update seamlessly without losing DOM state (e.g., expanded accordions).