no. you should build a test database on the a supported server.
you can either copy tables with restrictions or restore and delete data.
back this up and an restore on your limited box.
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Microsoft.Data.SqlClient.SqlError: CREATE DATABASE or ALTER DATABASE failed because the resulting cumulative database size would exceed your licensed limit of 10240 MB per database. (Microsoft.SqlServer.SmoExtended)
no. you should build a test database on the a supported server.
you can either copy tables with restrictions or restore and delete data.
back this up and an restore on your limited box.
First SSMS does not say anything. The message comes from SQL Server. SSMS is only the tool you use to talk to SQL Server.
Apparently, you have SQL Server Express Edition and Express is limited to a database size of 10 GB. If is after all a free edition that is licensed for production use.
If this is only for testing you can download and install Developer Edition, which is also free and which has no limits, but which is not licensed for production use.
You can not restore only a part of a backup. As Bruce says, you could restore on a different edition, delete tables you don't need, shrink the database in size below 10GB and take a new backup. Or copy data to a new database.