Quote
App needs a purely local MySQL ...
MySQL is not "just" file.
It's a running
process that serves requests from your App.
That process must be installed and running on the client device - that's
not your call.
If you really need something that's purely local, you might need to look at alternatives, like SQLite.
Quote
I wish to use Visual Studio C#.
Despites attempts by Our Friends in Redmond to make the .Net Framework "Open Source" and all that, you'll probably be limited to
.Net Core on non-Windows platforms, which may [heavily] restrict what you can do.
Quote
All my attempts either attempt to use localhost ...
That would suggest that you're using one of the "Web Application" Templates in 'Studio, which of course means that you'll need to have a Web Server [process] installed and running on the client device - again,
not your call.
Trying to do anything
truly portable across platforms is really, really hard. This is why so few companies try to do this any more. They just put everything on The Web, running everything as Web Applications on their own [virtualised] hardware and everybody else just uses them.
Regards, Phill W.