You are correct that SQL Server 2014 was the last version to include a 32-bit (x86) edition of the database engine. From SQL Server 2016 onward, Microsoft discontinued 32-bit builds entirely for the database engine itself, offering only 64-bit versions. The only 32-bit components that remain available in later releases are client tools such as SQL Server Management Studio and ODBC drivers, not the actual server engine.
If your Veritas Backup Exec installer is designed to install or connect to a 32-bit SQL Server instance, you will need to use SQL Server 2014 Express . SQL Server 2014 Express 32-bit can still run on a 64-bit operating system through Windows’ WOW64 subsystem, so you are not restricted to an older OS.
If the program itself cannot create a new database, you can manually attach or restore an existing database using SQL Server Management Studio 2014 Express. Alternatively, if you were hoping to upgrade to a newer SQL Server release, that will only be possible if your version of Backup Exec supports connecting to a 64-bit SQL instance.
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hth
Marcin