MSB4020: The value "" of the "Project" attribute in element <Import> is invalid
I finally figured out that after the Paket restore, I could run this command on only the new .NET Core project, thereby avoiding the errors from the other projects in the solution.
dotnet restore TheProject
Then the missing file was generated before compile, and the rest of the build script ran to completion.
PS (edit): This is not a perfect solution for me, because I have to add that line to my build script for every .NET Standard and .NET Core project in my solution. Having to maintain the script like that is not ideal. For that reason I will look into what has to be done to get rid of the MSB4020 error. Until then, this serves as a good workaround.