How to connect sql server express database to VS 2017

Figured out my issue: in Visual Studio's "Add New Data Source" wizard, the option I kept choosing was "Microsoft SQL Server Database File", because its description is "Use this selection to attach a database file to a local Microsoft SQL Server instance (including Microsoft SQL Express) using the .NET Framework Data Provider for SQL Server."

However, and I'm not sure why, this was not the right selection.

I tried selecting "other" instead.

Then on the next page input ".\SQLExpress" as the Server Name (mentioned on connectionstrings.com/sql-server/ ...Thanks for the lead @ryguy72!)

Then, under "Connect to a database" my local list of databases popped up, including the one I had created already using SSMS.

Test Connection finally worked then!