feat(frontend): update sessions page for enhanced health monitoring

- Add new status badges: 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
- Update health polling to check all active instances
- Only show Recreate Tunnel button for unreachable tunnels

openspec/changes/instance-health-monitoring/specs/smart-tunnel-recovery/spec.md

@@ -0,0 +1,45 @@
+## ADDED Requirements
+
+### Requirement: Tunnel failure classification
+The system SHALL distinguish tunnel failures from application errors when determining whether to recreate a tunnel.
+
+#### Scenario: Tunnel is broken
+- **GIVEN** a running instance with a tunnel URL
+- **WHEN** the health check receives one of:
+  - Connection refused (ECONNREFUSED)
+  - Connection timeout (ETIMEDOUT)
+  - DNS resolution failure (ENOTFOUND)
+  - Empty response
+- **THEN** the tunnel status is "unreachable"
+- **AND** the frontend shows a "tunnel error" badge
+- **AND** the "Recreate Tunnel" button is enabled
+
+#### Scenario: Application returns error
+- **GIVEN** a running instance with a tunnel URL
+- **WHEN** the health check receives HTTP 502, 503, or 504
+- **THEN** the tunnel status is "error_response"
+- **AND** the frontend shows an "app error" badge
+- **AND** the "Recreate Tunnel" button is NOT shown
+- **AND** the status code is displayed for diagnostics
+
+#### Scenario: Application is healthy
+- **GIVEN** a running instance with a tunnel URL
+- **WHEN** the health check receives HTTP 200-399
+- **THEN** the tunnel status is "healthy"
+- **AND** no error badge is shown
+
+#### Scenario: Tunnel recreates successfully
+- **GIVEN** an instance with a broken tunnel (status "unreachable")
+- **WHEN** the user clicks "Recreate Tunnel"
+- **THEN** the old cloudflared process is stopped
+- **AND** a new cloudflared process is started
+- **AND** the instance URL is updated
+- **AND** the tunnel status becomes "healthy" (after verification)
+
+## MODIFIED Requirements
+
+None.
+
+## REMOVED Requirements
+
+None.