So, I answered based on what I know about .NET which should be relevant to the question.
Others can be more clear on what is the same, similar, or different between .NET and .NET Core. Then the parts of .NET Core that are also in .NET can get something of a clean bill of health from me.
Sounds like .NET Core is aimed mostly just at the Linux world or the mobile world or people who want to be able to run the same code on both Linux and Windows. But I'm staying with Windows desktop and Windows Server -- already spent too much on getting good enough with Windows.
I have to suspect that Microsoft will continue to support Windows developers, including with VB.NET. If all Microsoft does with VB.NET is fix bugs, then fine with me. I'm not sure I have yet found a bug; so, fixing bugs in VB.NET should be easy enough for Microsoft.
I'm not really a programmer; instead I'm an applied mathematician and business man who also writes software. Since this thread is about startups, the core of my startup is some applied math I derived -- and then programmed, with a Web site for the users.
I would guess that if Microsoft wants all their major languages to run on both Windows and Linux, then that will be a lot of work and something for the future that I don't have to worry about.
While I don't like the C# C-like syntax, I could use C# if I needed to. IIRC there is a source code translator from VB --> C# and, maybe, if possible, in the other direction. So, I could convert my code to C#.
I suspect that I'm not the only developer who wants to continue with VB.NET and the .NET Framework as they have been for some years now. If the .NET Core is not relevant to such developers, then so be it, and that's not a good reason for Microsoft to abandon their old developers.