However my new host allows to import sql db backup-files (.BAK) only;
SQL Azure doesn't provide a native way to generate '.bak' format backup file. If you did need this format file, you could import the BACPAC File to a local SQL Server which supports importing BACPAC File. After that, a new User Database will be created. Then you could generate a '.bak' format file from the local SQL Server.
In addition, you also could try a tool named SqlAzureBakMaker which could make '.bak' file for you easily.
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