### 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
if (p_resource->get_path().is_resource_file()) {
			file->set_current_file(p_resource->get_path().get_file());
		} else {
			if (extensions.size()) {
				String resource_name_snake_case = p_resource->get_class().to_snake_case();
				file->set_current_file("new_" + resource_name_snake_case + "." + preferred.front()->get().to_lower());
			} else {
				file->set_current_file(String());
			}
		}
	} else if (!p_resource->get_path().is_empty()) {
		file->set_current_path(p_resource->get_path());
		if (extensions.size()) {
			String ext = p_resource->get_path().get_extension().to_lower();
			if (extensions.find(ext) == nullptr) {
				file->set_current_path(p_resource->get_path().replacen("." + ext, "." + extensions.front()->get()));
			}
		}
	} else if (preferred.size()) {
		String existing;
		if (extensions.size()) {
			String resource_name_snake_case = p_resource->get_class().to_snake_case();
			existing = "new_" + resource_name_snake_case + "." + preferred.front()->get().to_lower();
		}
		file->set_current_path(existing);
	}
	file->set_title(TTR("Save Resource As..."));
	file->popup_file_dialog();
}
void EditorNode::_menu_option(int p_option) {