Hi @sevelev,
Welcome to our community! 
Please follow the instruction on this website and make sure all required extensions are installed: https://code.visualstudio.com/docs/other/unity
If the issue persists, please check the console of VS Code (not Unity!). If the .NET Framework 4.7.1 (Developer Pack) is mentioned there, download and install it from the official Microsoft. Here is the link: https://dotnet.microsoft.com/download/dotnet-framework/net471
Depending on your version of Unity, it might be that you will have to install the “Visual Studio Code Editor” package in Window > Package Manager in Unity.
Maybe you’ll have to reboot your computer. Then launch Unity again and open one of your scripts.
Did this help you fix the issue?
See also:
- Forum User Guides : How to mark a topic as solved
I had the same problem. This person solved my issue! VS Code error C# and .NET Core (section 1) - #13 by systemeffect
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