After fixing my problem as mentioned here I am getting the below exception
System.IO.FileNotFoundException: \'Could not load file or assembly \'System
I guess you may have figured it out already but hope it would save someone precious time
In order to make everything work you would need to reference System.Data.SqlClient in WebApp .NET Framework 4.6.1 project that is referencing your .NET Standard Library. After that everything should work just fine.
Sounds like .NET Standard Library haven't grabbed with itself dependent library binary. There is nothing like "Copy Local" option in .NET Standard references so I don't see any way to check or set this behavior too