How do I create a fullscreen window with title bar on my second monitor?

Processing Coding Questions
1

The title describes the problem.

I can use fullScreen() to cover the screen with a window on any monitor. But it doesn’t have a title bar.

The following code creates a window with a title bar that covers the screen. But only for the default monitor. (Also, the positioning is wrong, since a bug persists from years ago.)

void settings() {
    size(displayWidth, displayHeight);
}

void setup() {
    surface.setTitle("my application");
    surface.setLocation(0, 0);
}

void draw() {
    background(0);
    fill(200);
    circle(mouseX, mouseY, width/4.);
}