### 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
slider->set_v_size_flags(SIZE_SHRINK_CENTER);
	slider->set_focus_mode(FOCUS_NONE);
	gc->add_child(slider);
	SpinBox *val = memnew(SpinBox);
	slider->share(val);
	val->set_select_all_on_focus(true);
	gc->add_child(val);
	LineEdit *vle = val->get_line_edit();
	vle->connect("text_changed", callable_mp(this, &ColorPicker::_text_changed));
	vle->connect("gui_input", callable_mp(this, &ColorPicker::_line_edit_input));
	vle->set_horizontal_alignment(HORIZONTAL_ALIGNMENT_RIGHT);
	val->connect("gui_input", callable_mp(this, &ColorPicker::_slider_or_spin_input));
	slider->set_h_size_flags(SIZE_EXPAND_FILL);
	slider->connect("drag_started", callable_mp(this, &ColorPicker::_slider_drag_started));
	slider->connect("value_changed", callable_mp(this, &ColorPicker::_slider_value_changed).unbind(1));
	slider->connect("drag_ended", callable_mp(this, &ColorPicker::_slider_drag_ended).unbind(1));
	slider->connect("draw", callable_mp(this, &ColorPicker::_slider_draw).bind(idx));
	slider->connect("gui_input", callable_mp(this, &ColorPicker::_slider_or_spin_input));
	if (idx < SLIDER_COUNT) {
		sliders[idx] = slider;
		values[idx] = val;
		labels[idx] = lbl;
	} else {
		alpha_slider = slider;
		alpha_value = val;
		alpha_label = lbl;
	}
}
#ifdef TOOLS_ENABLED
void ColorPicker::set_editor_settings(Object *p_editor_settings) {