Backup-restore is not directly supported by standard methods in SQL Server/Azure SQL database. One possible way to backup a tenant could be to have a script, which could bcp data to text files. Restore could similarly be a script, which could bcp from txt files to tables in the destination database. Both scripts could be auto-generated from tenant metadata. If the schema for a tenant has 100 tables, the number of tables in a database in this model grows quickly, and the administrative cost of maintaining scripts and tenant metadata could be high. As a side note, no query execution plans can be reused across tenants, since table names are different.
Thinking about customers which share schema, tables, etc. but need to be handled differently requires some additional effort; pretty much all of the tools around SQL Server assume that you care about things at the table, filegroup, or database level.