Here's an additional solution working on Visual Studio 2019 as of the date of this post. This will copy the folder structure recursively and all files within. Tested on a C++ .vcxproj in a multi-project solution.
First, start by editing your [ .proj / .vcxproj / .csproj ] file. Once open, find your project scoped tag. If you already have ItemGroups within, then paste the code below directly after the existing ones. Otherwise, add it in before the PropertyGroup tags. Then modify the Include & Link parameters for the folder structure you wish to copy to the output path.
<ItemGroup>
<Content Include="..\Assets\**\*.*">
<CopyToOutputDirectory>PreserveNewest</CopyToOutputDirectory>
<DeploymentContent>true</DeploymentContent>
<Link>Assets\%(RecursiveDir)\%(Filename)%(Extension)</Link>
</Content>
</ItemGroup>
Note: If you have multiple top level folders, like JS, IMG, BIN, etc., then create a new entry for each one.