How can I use edgesIgnoringSafeArea in SwiftUI, but make a child view respect the safe area?

Whatever view you draw in the background modifier will use the frame of the view it's modifying. So you need to tell THAT view to ignore the safe area.

.background(Color.blue.edgesIgnoringSafeArea(.bottom))

You can access the height of the safe area using a GeometryReader. Then you could use the height of the safe area as bottom padding or offset on your button.
https://developer.apple.com/documentation/swiftui/geometryproxy

struct ContentView: View {
    var body: some View {

        GeometryReader { proxy in
            ZStack(alignment: .bottom) {

                List {
                    Text("Item 1")
                    Text("Item 2")
                    Text("Item 3")
                }

                HStack {
                    Spacer()
                    Button(action: {
                        // do something
                    }){
                        Text("Button")
                            .font(.title)
                            .padding()
                            .background(Color.green)
                            .foregroundColor(.white)
                            .cornerRadius(15)
                    }
                    .padding(.bottom, proxy.safeAreaInsets.top)
                    Spacer()
                }.background(Color.blue)
            }.edgesIgnoringSafeArea(.bottom)
        }
    }
}