### 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
bool ret_changed = false;
	List<PropertyInfo> pi;
	obj->get_property_list(&pi);
	for (const PropertyInfo &E : pi) {
		if (!(E.usage & PROPERTY_USAGE_STORAGE)) {
			continue;
		}
		switch (E.type) {
			case Variant::OBJECT: {
				Ref<Resource> res = obj->get(E.name);
				if (_find_and_save_resource(res, processed, flags)) {
					ret_changed = true;
				}
			} break;