You have a nested observable object.

class ClassB: ObservableObject {
    @Published var board: [[ClassC]]
}

class ClassC: ObservableObject {
    @Published var color: Color = .white
}

A limitation of SwiftUI is that it won't detect changes to nested observable objects. In your case the changes to the color property in ClassC will not be update board in ClassB. This is a common problem people run into in SwiftUI. If you enter SwiftUI nested observable object in a search engine, you will find many articles about the problem with nested observable objects and strategies for dealing with the problem.

The solution in your code is relatively simple. Since ClassC only contains a color, you can make board an array of Color arrays and get rid of ClassC.

class ClassB: ObservableObject {
    @Published var board: [[Color]]
}