To your point, a simpler solution would be to use Azure Monitor Metrics. Though I do not see replication as a metric at a glance. If this does not work you might try adding it as a custom metric in diagnostic settings. Also, this could be run as an automation runbook or possibly a logic app to log the output or send as an email.
https://learn.microsoft.com/en-us/azure/storage/common/storage-monitoring-diagnosing-troubleshooting?tabs=dotnet#monitoring-performance
https://learn.microsoft.com/en-us/azure/storage/common/storage-insights-overview
https://learn.microsoft.com/en-us/azure/azure-monitor/alerts/alerts-metric