CI: Replication problem detection tests

[renecannao]

Summary

Orchestrator's core value is detecting replication problems. We have no tests that verify problem detection works correctly.

Proposed Tests

• Stop replication on a replica, verify orchestrator detects ReplicationStopped
• Introduce replication lag (lock tables on replica), verify lag detection
• Set a replica to read_only=0 (when it should be RO), verify problem detected
• Verify /api/problems endpoint returns detected problems with correct analysis
• Clear the problem (restart replication), verify it disappears from problems list

Acceptance Criteria

• At least 3 problem types are tested (stopped replication, lag, read_only mismatch)
• Tests verify problems appear AND clear correctly
• Tests integrated into CI workflow

[coderabbitai]

🔗 Related PRs

#51 - Add functional test CI: Docker MySQL topology + ProxySQL + failover tests [merged]

---

📝 Issue Planner

_{Check the box below or use the @coderabbitai plan command to generate an implementation plan and prompts that you can use with your favorite coding assistant.}

• Create Plan

---

🧪 Issue enrichment is currently in open beta.

You can configure auto-planning by selecting labels in the issue_enrichment configuration.

To disable automatic issue enrichment, add the following to your .coderabbit.yaml:

issue_enrichment:
  auto_enrich:
    enabled: false

💬 Have feedback or questions? Drop into our discord!