### 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 (!scene_path.is_empty()) {
						required_load_paths.push_front(scene_path);
					}
					Ref<SceneState> inherited_state = original_node->get_scene_inherited_state();
					while (inherited_state.is_valid()) {
						String inherited_path = inherited_state->get_path();
						
						if (!inherited_path.is_empty()) {
							required_load_paths.push_front(inherited_path);
						}
						inherited_state = inherited_state->get_base_scene_state();
					}
					
					
					for (String path : required_load_paths) {
						if (!local_scene_cache.find(path)) {
							current_packed_scene = ResourceLoader::load(path, "", ResourceFormatLoader::CACHE_MODE_REPLACE, &err);
							local_scene_cache[path] = current_packed_scene;
						} else {
							current_packed_scene = local_scene_cache[path];
						}
					}
				}
				ERR_FAIL_COND(current_packed_scene.is_null());
				
				Node *instantiated_node = nullptr;
				if (current_packed_scene.is_valid()) {
					instantiated_node = current_packed_scene->instantiate(PackedScene::GEN_EDIT_STATE_INSTANCE);
				}