ADDITIONAL SYSTEM INFORMATION :
All Java versions including the most recent release
Apple M2
MacOS Ventura 13.6.5 (22G621)

A DESCRIPTION OF THE PROBLEM :
Two modal dialogs displayed one after another disable disable screen menu items.
I observed this behavior occurred after I updated my OS from 13.6.4 to 13.6.5.

STEPS TO FOLLOW TO REPRODUCE THE PROBLEM :
Run the application below.
Execute action "Click me" from the menu "Run".
Observe and confirm 2 confirmation messages by clicking on "Ok".
After the second message is confirmed, try to access the menu action again.

EXPECTED VERSUS ACTUAL BEHAVIOR :
EXPECTED -
The menu actions should remain available.
ACTUAL -
The menu action is grayed out.

---------- BEGIN SOURCE ----------
import javax.swing.JFrame;
import javax.swing.JMenu;
import javax.swing.JMenuBar;
import javax.swing.JMenuItem;
import javax.swing.JOptionPane;
import javax.swing.JLabel;
import java.awt.BorderLayout;

public class MainFrame extends JFrame {
    public MainFrame() {
        System.setProperty("apple.laf.useScreenMenuBar", "true");
        this.setSize(300, 200);
        this.setDefaultCloseOperation(JFrame.EXIT_ON_CLOSE);
        this.setLayout(new BorderLayout());

        // Create menu bar
        JMenuBar menuBar = new JMenuBar();

        // Create a menu
        JMenu runMenu = new JMenu("Run");

        // Create a menu item
        JMenuItem clickMeItem = new JMenuItem("Click me");

        // Add action listener to menu item
        clickMeItem.addActionListener(e -> {
            JOptionPane.showMessageDialog(this, "The application menu becomes disabled");
            JOptionPane.showMessageDialog(this, "The application menu remains disabled after the focus goes back to the main frame");
        });

        // Add menu item to menu
        runMenu.add(clickMeItem);

        // Add menu to menu bar
        menuBar.add(runMenu);

        // Set the menu bar
        this.setJMenuBar(menuBar);

        // Add a label to display text in the middle of the frame
        JLabel label = new JLabel("Execute \"Run->Click me\"", JLabel.CENTER);
        this.add(label, BorderLayout.CENTER);
    }

    public static void main(String[] args) {
        javax.swing.SwingUtilities.invokeLater(() -> {
            MainFrame frame = new MainFrame();
            frame.setVisible(true);
        });
    }
}
---------- END SOURCE ----------

CUSTOMER SUBMITTED WORKAROUND :
1. The menu is reenabled after user changes to another application and activates this application again.
2. The menu is reenabled if you add

            final MenuBar awtMenubar = getMenuBar();
            setMenuBar(null);
            setMenuBar(awtMenubar);

after the second call of JOptionPane.showMessageDialog

FREQUENCY : always