doctor: complete runtime check documentation sprint

Signed-off-by: master <>

docs/doctor/articles/servicegraph/servicegraph-mq.md

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+---
+checkId: check.servicegraph.mq
+plugin: stellaops.doctor.servicegraph
+severity: warn
+tags: [servicegraph, messaging, rabbitmq, connectivity]
+---
+# Message Queue Connectivity
+
+## What It Checks
+Reads `RabbitMQ:Host` or `Messaging:RabbitMQ:Host` plus an optional port, defaulting to `5672`, and attempts a TCP connection.
+
+The check skips when RabbitMQ is not configured and fails on timeouts, DNS failures, or refused connections.
+
+## Why It Matters
+Release tasks, notifications, and deferred work often depend on a functioning message broker. A dead queue path turns healthy APIs into backlogged systems.
+
+## Common Causes
+- `RabbitMQ__Host` is unset or points to the wrong broker
+- The broker container is down
+- AMQP traffic is blocked between Doctor and RabbitMQ
+
+## How to Fix
+
+### Docker Compose
+```yaml
+services:
+  doctor-web:
+    environment:
+      RabbitMQ__Host: rabbitmq
+      RabbitMQ__Port: "5672"
+```
+
+```bash
+docker compose -f devops/compose/docker-compose.stella-ops.yml ps rabbitmq
+docker compose -f devops/compose/docker-compose.stella-ops.yml logs --tail 100 rabbitmq
+docker compose -f devops/compose/docker-compose.stella-ops.yml exec doctor-web sh -lc "nc -zv rabbitmq 5672"
+```
+
+### Bare Metal / systemd
+```bash
+nc -zv <rabbit-host> 5672
+```
+
+### Kubernetes / Helm
+```bash
+kubectl exec deploy/doctor-web -n <namespace> -- sh -lc "nc -zv <rabbit-service> 5672"
+```
+
+## Verification
+```bash
+stella doctor --check check.servicegraph.mq
+```
+
+## Related Checks
+- `check.servicegraph.valkey` - cache and queue connectivity usually fail together when service networking is broken
+- `check.servicegraph.timeouts` - aggressive timeouts can make a slow broker look unavailable