Hello yirgalem asore
For Azure AQL managed instance whenever the drop database statement is executed in AZURE SQL MI, it internally performs the Tail Log Backup of that database. The database's drop operation had stopped and not progressing forward because the Tail Log Backup InProgress operation was preventing DB drop requests.
To resolve this, verify the database is listed if you execute this PowerShell cmdlet
Get-AzSqlInstanceDatabase -InstanceName "name" -ResourceGroupName "resourcegroupname"
and if you see the database listed on the result of the PowerShell cmdlet, then use this other PowerShell cmdlet to remove the database.
Remove-AzSqlInstanceDatabase -Name "Database01" -InstanceName "managedInstance1" -ResourceGroupName "ResourceGroup01"
Also you can try by restarting the SSMS.
If the issue persists, please don't hesitate to reach out for further assistance.
I hope this has been helpful! Kindly consider upvoting the Answer if the information provided is helpful. This can assist other community members in resolving similar issues. Happy to help you.