Greetings!
There is no way to download LTR backup directly from Azure Storage.
You should follow Long-term backup retention - Azure SQL Database & Azure SQL Managed Instance | Microsoft Learn to configure LTR backup policy before deleting resource group.
And should use PowerShell command to get details information about LTR backups after deleting resource group.
For more information, you can refer to Azure SQL Database: Manage long-term backup retention - Azure SQL Database | Microsoft Learn and Get-AzSqlDatabaseLongTermRetentionBackup (Az.Sql) | Microsoft Learn
Regards
Geetha