feat(health-monitoring): complete instance health monitoring implementation

Backend:
- Container startup verification with docker inspect polling
- Readiness probe integration with ToolType configuration
- Enhanced health endpoint checking container + tunnel status
- Smart tunnel recovery distinguishing connection errors vs HTTP errors
- New status states: starting, probing, unhealthy

Frontend:
- Updated status badges for new states (starting, probing, unhealthy)
- Show tunnel error only when tunnel_status is unreachable
- Show app error badge with status code for error_response
- Add collapsible probe output section for diagnostics
- Only show Recreate Tunnel button for unreachable tunnels

Quality Gates:
- Frontend type checking: PASSED
- Frontend build: PASSED
- Backend unit tests: 56 passed

Addresses instance-health-monitoring OpenSpec change

apps/web/src/api/sessions.ts

@@ -106,13 +106,13 @@ export async function getUserSessions(): Promise<Session[]> {
 export interface InstanceHealth {
   healthy: boolean;
   container_status: string;
-  container_health?: string;
-  container_exit_code?: number | null;
+  container_health: string | null;
+  container_exit_code: number | null;
   tunnel_status: string;
   tunnel_status_code: number | null;
   probe_status: string;
-  last_probe_output?: string;
-  error?: string;
+  last_probe_output: string | null;
+  error: string | null;
 }
 
 export async function checkInstanceHealth(

apps/web/src/pages/sessions.tsx

@@ -119,9 +119,11 @@ export const SessionsPage = () => {
             [session.id]: {
               healthy: false,
               container_status: "unknown",
+              container_health: null,
               tunnel_status: "unreachable",
               tunnel_status_code: null,
               probe_status: "unknown",
+              last_probe_output: null,
               error: "check failed",
             },
           }));