You can not just migrate a backup from Sql Server to Aurora. There are two optins you can consider
1/ Use SCT and DMS to migrate your Sql Server database to Aurora.
There are two parts for heterogeneous migration, Schema conversion and data migration. SCT ( Schema Conversion Tool) as the name implies is a tool to convert your database objects from one db engine to another and then you can use DMS to migrate your data from Sql Server to Aurora.
2/ Use babelfish endpoint and then use dms to migrate your data into Aurora.
I hope it helps.
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