### 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
Control *drag_control = memnew(Control);
	TextureRect *drag_preview = memnew(TextureRect);
	Label *label = memnew(Label);
	Ref<Texture2D> preview;
	{
		
		Ref<ImageTexture> texture = theme->get_icon(SNAME("FileBigThumb"), EditorStringName(EditorIcons));
		Ref<Image> img = texture->get_image();
		img = img->duplicate();
		img->resize(48, 48); 
		preview = ImageTexture::create_from_image(img);
	}
	drag_preview->set_texture(preview);
	drag_control->add_child(drag_preview);
	if (p_res->get_path().is_resource_file()) {
		label->set_text(p_res->get_path().get_file());
	} else if (!p_res->get_name().is_empty()) {
		label->set_text(p_res->get_name());
	} else {
		label->set_text(p_res->get_class());
	}
	drag_control->add_child(label);
	p_from->set_drag_preview(drag_control); 
	label->set_position(Point2((preview->get_width() - label->get_minimum_size().width) / 2, preview->get_height()));
	Dictionary drag_data;
	drag_data["type"] = "resource";
	drag_data["resource"] = p_res;
	drag_data["from"] = p_from;