fix: add Router+LiteLLM+PVE API probes to infrastructure-monitoring check-health

- Added Router health probe (http://192.168.68.116/health) — expected 200
- Added LiteLLM health probe (http://192.168.68.116/litellm/health) — expected 200
- Added PVE API probe (https://192.168.68.116:8006/api2/json) — 401 expected for unauthenticated
- Clarified that 401 means API is up, 000 means unreachable, 500 means API down

Closes: infra-monitoring-probe-alignment

infrastructure-monitoring.prose.md

@@ -122,6 +122,18 @@ curl -s http://192.168.68.8:9400/metrics && echo " - OK" || echo " - FAIL"
 curl -s http://192.168.68.110:9400/metrics && echo " - OK" || echo " - FAIL"
 curl -s http://192.168.68.15:9400/metrics && echo " - OK" || echo " - FAIL"
 
+# Router health (via nginx on port 80)
+curl -s -o /dev/null -w '%{http_code}' http://192.168.68.116/health
+# Expected: 200 (Router is up and responding)
+
+# LiteLLM health (via nginx on port 80)
+curl -s -o /dev/null -w '%{http_code}' http://192.168.68.116/litellm/health
+# Expected: 200 (LiteLLM is up and responding)
+
+# PVE API (401 expected for unauthenticated probe — API is up over https)
+curl -s -o /dev/null -w '%{http_code}' https://192.168.68.116:8006/api2/json
+# Expected: 401 (unauthorized — API is up; 000 = unreachable, 500 = API down)
+
 # Prometheus targets
 curl -s http://192.168.68.116:9090/api/v1/targets | jq '.data.activeTargets'
 # Expected: All targets UP (may show some down if exporters not deployed)
@@ -130,7 +142,7 @@ curl -s http://192.168.68.116:9090/api/v1/targets | jq '.data.activeTargets'
 curl -s http://192.168.68.116:3001/api/health | jq '{status, version}'
 # Expected: {"status":"ok","version":"..."}
 
-# LiteLLM metrics
+# LiteLLM metrics (Prometheus endpoint)
 curl -s http://192.168.68.116:4001/metrics | head -20
 # Expected: Prometheus-formatted metrics output
 ```