How do I get .NET Core projects to copy NuGet references to the build output?

You can use PostBuildEvent to automate module deployment on build.

To get NuGet assemblies in build folder add in csproj of your module

<PropertyGroup>
    <CopyLocalLockFileAssemblies>true</CopyLocalLockFileAssemblies>
</PropertyGroup>

Define what module files you want where using Include/Exclude (modify path as necessary)

<ItemGroup>
    <ModuleFiles
      Include="$(TargetDir)*.dll"
      Exclude="$(TargetDir)System*.dll;$(TargetDir)Microsoft*.dll"
      DestinationPath="$(SolutionDir)src\MyProject\Modules\MyModule\%(Filename)%(Extension)">
    </ModuleFiles>
</ItemGroup>

Reset your build folder to default and add PostbuildEvent

<Target Name="PublishModule" AfterTargets="PostBuildEvent" Inputs="@(ModuleFiles)" Outputs="@(ModuleFiles->'%(DestinationPath)')">
    <WriteLinesToFile File="$(SolutionDir)src\[YOURAPP]\app_offline.htm" />
    <Copy SourceFiles="@(ModuleFiles)" DestinationFiles="@(ModuleFiles->'%(DestinationPath)')" />
    <Delete Files="$(SolutionDir)src\[YOURAPP]\app_offline.htm" />
</Target>

I'm including app_offline to recycle app if it's already running to avoid file in use errors.

You can add this to a <PropertyGroup> inside your csproj file to enforce copying NuGet assemblies to the build output:

<CopyLocalLockFileAssemblies>true</CopyLocalLockFileAssemblies>

However, note that the build output (bin/Release/netcoreapp*/*) is not supposed to be portable and distributable, the output of dotnet publish is. But in your case, copying the assemblies to the build output is probably very useful for testing purposes. But note that you could also use the DependencyContext api to resolve the DLLs and their locations that are part of the application's dependency graph instead of enumerating a local directory.