Problem is the same as described in 6838089, 6838942.
Please see the following code:
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import javax.swing.*;
import java.awt.*;
import static java.lang.System.out;

public class SettingBackground {
    public static void main(String[] args) {
        SwingUtilities.invokeLater(new Runnable() {
            @Override
            public void run() {
                GraphicsEnvironment ge = GraphicsEnvironment.getLocalGraphicsEnvironment();
                GraphicsDevice[] devices = ge.getScreenDevices();
                Frame window = new Frame("My frame");
                window.setBackground(Color.RED);
                GraphicsDevice device = devices[0];
                out.println("using device " + device);
                device.setFullScreenWindow(window);
                out.println("device.getFullScreenWindow() = " + device.getFullScreenWindow());
                try {
                    window.setBackground(new Color(30,30,30,100));
                    System.out.println("No IllegalComponentStateException");
                    GraphicsConfiguration gc = window.getGraphicsConfiguration();
                    out.println("device = " + gc.getDevice());
                    out.println("device.getFullScreenWindow() = " + gc.getDevice().getFullScreenWindow());
                    // onbe can see elliptical shape of the window
                    Thread.sleep(1000);
                } catch (IllegalComponentStateException e) {
                    System.out.println("OK - IllegalComponentStateException thrown");
                } catch (InterruptedException e) {
                } finally {
                    window.dispose();
                }
            }
        });
    }
}

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On two-monitor configuration it prints out:

using device Win32GraphicsDevice[screen=0]
device.getFullScreenWindow() = java.awt.Frame[frame0,1280,0,1280x1024,layout=java.awt.BorderLayout,title=My frame,resizable,normal]
No IllegalComponentStateException
device = Win32GraphicsDevice[screen=1]
device.getFullScreenWindow() = null
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