Steps to reproduce:

Run the code:
-----------------------
import javax.swing.*;
import com.sun.java.swing.plaf.gtk.GTKLookAndFeel;

public class GnomeHiDPITest {

    public static void main(String[] args) {
        SwingUtilities.invokeLater(() -> {
            try {
                UIManager.setLookAndFeel(new GTKLookAndFeel());
                JFrame frame = new JFrame();
                frame.setSize(100, 100);
                frame.setDefaultCloseOperation(JFrame.EXIT_ON_CLOSE);
                JMenuBar menuBar = new JMenuBar();
                menuBar.add(new JMenu("Test 1"));
                menuBar.add(new JMenu("Test 2"));
                frame.setJMenuBar(menuBar);
                frame.setVisible(true);
            } catch (UnsupportedLookAndFeelException ex) {
                throw new RuntimeException(ex);
            }
        });
    }
}
-----------------------

- Enable HiDPI
> gsettings set org.gnome.desktop.interface scaling-factor 2

The text menu size is enlarged.

Note that under Metal L&F the text size is not changed.