Automated backups are used to recover deleted databases and the retention policies for backups is 7 days for Basic and 35 days for Standard and Premium. Here you will find more information.
If you delete the Azure SQL Database logical server also or its resorce group, then you need to create an Azure Support ticket to recover the logical server and the database. There is no guarantee for for recovery on this scenario, the sooner you create the ticket the better on these cases.