Hi Alina,
What you can do is restore certain day to a brand-new database, export that database to BACPAC file, delete the brand-new database, download BACPAC file to local machine, import BACPAC to local SQL Server. In this way the new database will not exist for very long (minutes), so you will only be charged a small amount, especially for Basic.
Please see articles below for how to export to BACPAC and import the BACPAC file.
Export to a BACPAC file - Azure SQL Database and Azure SQL Managed Instance
https://learn.microsoft.com/en-us/azure/azure-sql/database/database-export?view=azuresql
Import a BACPAC File to Create a New User Database
After you are done downloading the BACPAC file you should delete it from the storage account so that charges don't continue to accrue.
Please click Accept Answer and upvote if the above was helpful. Add a comment below if something is unclear.
Thanks.
-TP