### Tested versions

v4.2.stable.official [46dc27791]

### System information

Windows 11- Godot v4.2.stable.official [46dc27791] - Vulkan (Forward+)

### Issue description

When I switch picker mode the next time I open it should be the pick mode I selected last time but it's not

https://github.com/godotengine/godot/assets/46812028/522c8b55-14cf-4781-963f-a465a03c9432



### Steps to reproduce

Toggle a picker mode off and on again

### Minimal reproduction project (MRP)

N/A
Ref<InputEventMouse> me = p_input;
	if (me.is_valid()) {
		Vector2 point = me->get_position();
		int nrect = -1;
		for (int i = 0; i < DOCK_SLOT_MAX; i++) {
			if (dock_select_rect[i].has_point(point)) {
				nrect = i;
				break;
			}
		}
		if (nrect != dock_select_rect_over_idx) {
			dock_select->queue_redraw();
			dock_select_rect_over_idx = nrect;
		}
		if (nrect == -1) {
			return;
		}
		Ref<InputEventMouseButton> mb = me;
		if (mb.is_valid() && mb->get_button_index() == MouseButton::LEFT && mb->is_pressed() && dock_popup_selected_idx != nrect) {
			dock_slot[nrect]->move_tab_from_tab_container(dock_slot[dock_popup_selected_idx], dock_slot[dock_popup_selected_idx]->get_current_tab(), dock_slot[nrect]->get_tab_count());
			if (dock_slot[dock_popup_selected_idx]->get_tab_count() == 0) {
				dock_slot[dock_popup_selected_idx]->hide();
			} else {
				dock_slot[dock_popup_selected_idx]->set_current_tab(0);
			}
			dock_popup_selected_idx = nrect;