gtkmm 4: Make widget to vertically fill the Gtk::HeaderBar

Question

Is it possible for a Gtk::Widget, say a Gtk::Button to fill the Gtk::HeaderBar completely vertically? If it is indeed possible, how is this achieved?

As seen in the above picture, there seems to be a small space between the top and bottom end of the HeaderBar, no matter if Button::set_vexpand(true), Button::set_margin(0), HeaderBar::set_margin(0) or HeaderBar::set_spacing(0) are called.