You get that error because that other computer has an older version of SQL Server installed. I don't recall exactly, but I believe that 852 is SQL 2017.
And if there is no SQL Server instance all, of course nothing will work.
How to deal with this situation, depends on the nature of the application. For a big multi-user application, you assume that SQL Server is installed somewhere on the network, and you only document the required version. (And the application permits the user to select which server to use.)
For a simple single-user application, that is not very convenient. Rather you should include SQL Server in your install. And if it is a true single-user application, LocalDB is a good choice.
However, rather than using AttachDBFilename, I think it is better to distribute a backup of the database and restore it to some location when you install LocalDB, so that the database is place once for all.