Controlling a popup QWidget attached to a QToolButton

I want to get a Popup Widget to be shown when clicking on a QToolbutton.

This can be done by adding an action to the button itself. The popup will contain a three buttons (update, create and cancel) and a text input field.

I have some sample code with only one button I have shared as a Github repository.

The most relevant part of the code is:

    auto button = new QToolButton(this);
    button->setText(" AA ");

    auto popup = new Popup(button, this);
    auto popupAction = new QWidgetAction(this);
    popupAction->setDefaultWidget(popup);
    button->setPopupMode(QToolButton::InstantPopup);
    button->addAction(popupAction);

The result is as follow:

I have two issues I cannot solve:

• Getting the popup widget to right align to the button.
• Getting the popup widget close when one of the buttons inside of it are clicked.

Right align the popup

There is already a similar question: Set position (to right) of Qt QPushButton popup menu.

I can add the suggested code:

void Popup::showEvent(QShowEvent*)
{
    QPoint p = this->pos();
    QRect geo = clickedButton->geometry();
    
    this->move(p.x()+geo.width()-this->geometry().width(), p.y());
}

But only the content of the popup gets right aligned to the button, not the popup itself:

Closing the popup

If I click anywhere (but a widget) in the Popup it closes. I'm somehow fine with this.

But if I cannot manage to get a click on the button to close the popup.
I've tried to call the close() function but it only clears the content of the popup without closing it.

Can I get the button to trigger a signal and then close the popup?