### 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
int scene_idx = -1;
	for (int i = 0; i < editor_data.get_edited_scene_count(); i++) {
		if (editor_data.get_scene_path(i) == p_path) {
			scene_idx = i;
			break;
		}
	}
	int current_tab = editor_data.get_edited_scene();
	if (scene_idx == -1) {
		if (get_edited_scene()) {
			
			EditorUndoRedoManager::get_singleton()->clear_history(false, editor_data.get_current_edited_scene_history_id());
		}
		return;
	}
	if (current_tab == scene_idx) {
		editor_data.apply_changes_in_editors();
		_save_editor_states(p_path);
	}
	
	_remove_scene(scene_idx, false);
	load_scene(p_path, true, false, true, true);
	
	editor_data.move_edited_scene_to_index(scene_idx);
	EditorUndoRedoManager::get_singleton()->clear_history(false, editor_data.get_scene_history_id(scene_idx));
	
	scene_tabs->set_current_tab(current_tab);
}
void EditorNode::find_all_instances_inheriting_path_in_node(Node *p_root, Node *p_node, const String &p_instance_path, List<Node *> &p_instance_list) {