My solution is structured as follows:
Tried this with a plain netcoreapp3.1 class library.
While in XAML Designer the ChessApp's MainWindow correctly shows the image resource, I see a System.Resources.MissingManifestResourceException at runtime.
Changing the class library project's Sdk property from
<Project Sdk="Microsoft.NET.Sdk">
to
<Project Sdk="Microsoft.NET.Sdk.WindowsDesktop">
fixed the problem.