### 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
ERR_FAIL_NULL(instantiated_node);
				bool original_node_is_displayed_folded = original_node->is_displayed_folded();
				bool original_node_scene_instance_load_placeholder = original_node->get_scene_instance_load_placeholder();
				
				instantiated_node->set_name(original_node->get_name());
				
				String original_node_file_path = original_node->get_scene_file_path();
				if (current_edited_scene == original_node) {
					instantiated_node->set_scene_instance_state(original_node->get_scene_instance_state());
					
					if (original_node_file_path.is_empty()) {
						Ref<SceneState> state = current_packed_scene->get_state();
						state->set_path(current_packed_scene->get_path());
						instantiated_node->set_scene_inherited_state(state);
						instantiated_node->set_scene_file_path(String());
					}
					editor_data.set_edited_scene_root(instantiated_node);
					current_edited_scene = instantiated_node;
					if (original_node->is_inside_tree()) {
						SceneTreeDock::get_singleton()->set_edited_scene(current_edited_scene);
						original_node->get_tree()->set_edited_scene_root(instantiated_node);
					}
				}
				
				original_node->replace_by(instantiated_node, false);
				
				original_node->queue_free();
				
				instantiated_node->set_display_folded(original_node_is_displayed_folded);
				instantiated_node->set_scene_instance_load_placeholder(original_node_scene_instance_load_placeholder);