### 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
String item_text;
	if (p_renderer_name == "forward_plus") {
		item_text = TTR("Forward+");
	}
	if (p_renderer_name == "mobile") {
		item_text = TTR("Mobile");
	}
	if (p_renderer_name == "gl_compatibility") {
		item_text = TTR("Compatibility");
	}
	if (p_mark_overridden) {
		item_text += " " + TTR("(Overridden)");
	}
	renderer->add_item(item_text);
}
void EditorNode::_resource_saved(Ref<Resource> p_resource, const String &p_path) {
	if (singleton->saving_resources_in_path.has(p_resource)) {
		
		return;
	}
	if (EditorFileSystem::get_singleton()) {
		EditorFileSystem::get_singleton()->update_file(p_path);
	}
	singleton->editor_folding.save_resource_folding(p_resource, p_path);
}
void EditorNode::_resource_loaded(Ref<Resource> p_resource, const String &p_path) {