Thank you for reaching out.
My understanding is that you are trying to get the list of deleted and drop Synapse DBs.
I would suggest enabling auditing from the azure portal, Set up Auditing for Azure SQL Database and Azure Synapse Analytics as first step then Use Auditing to analyze audit logs and reports.
You can start with a simple query, such as: search "SQLSecurityAuditEvents" to view the audit logs. From here, you can also use Azure Monitor logs to run advanced searches on your audit log data. Azure Monitor logs gives you real-time operational insights using integrated search and custom dashboards to readily analyze millions of records across all your workloads and servers.
Please use the query in the blog and modify it to get the correct result.
Helpful link https://learn.microsoft.com/en-us/azure/azure-monitor/logs/log-analytics-tutorial#view-table-information
Regards,
Oury