I am not clear on the association between a break glass account and Log Analytics? You can use logs to monitor and alert on account usage. https://learn.microsoft.com/en-us/azure/active-directory/roles/security-emergency-access
Azure Monitor workspaces (log analytics) are billed based on the volume of data ingested. This includes 31 days of retention. Most diagnostic logs are fairly inexpensive to collect. It really depends on the volume of data. These logs are readily accessible and are fairly easy to add alerts if needed. https://azure.microsoft.com/en-in/pricing/details/monitor
Azure Activity logs are free n Log Analytics, AAD audit logs are not.