Each library runs under the process of the main application. So the main application needs to know to load the SqlClient DLL. So the parent project (the .NET 4.7.1 project) needs to have SqlClient added as a reference, either by installing the NuGet package, or just adding a reference by browsing to the DLL under the .NET Standard project.
Old answer: That version exists in NuGet: https://www.nuget.org/packages/System.Data.SqlClient/4.4.0
In the Package Manager Console (make sure the ‘Default project’ drop-down is set to the right one), try uninstalling and then reinstalling that specific version:
Uninstall-Package System.Data.SqlClient
Install-Package System.Data.SqlClient -Version 4.4.0
Update: Or, in your binding redirect, just use 4.2.0.0 as the oldVersion.