Здесь же идет создание типа ByteArrayOutputStream byteArrayOutputStream = serializeSingletonInstance(instance); и этот же тип ByteArrayOutputStream передается в метод deserializeSingletonInstance(ByteArrayOutputStream byteArrayOutputStream), для чего использовать .toByteArray() если тип и так ByteArrayOutputStream?
public class Solution implements Serializable {
    public static void main(String[] args) throws IOException, ClassNotFoundException {
        Singleton instance = Singleton.getInstance();

        ByteArrayOutputStream byteArrayOutputStream = serializeSingletonInstance(instance);

        Singleton singleton = deserializeSingletonInstance(byteArrayOutputStream);
        Singleton singleton1 = deserializeSingletonInstance(byteArrayOutputStream);

        System.out.println("Проверка ourInstance : " + singleton.getInstance());
        System.out.println("Проверка ourInstance : " + singleton1.getInstance());
        System.out.println("=========================================================");
        System.out.println("Проверка singleton : " + singleton);
        System.out.println("Проверка singleton1 : " + singleton1);
    }

    public static ByteArrayOutputStream serializeSingletonInstance(Singleton instance) throws IOException {
        ByteArrayOutputStream byteArrayOutputStream = new ByteArrayOutputStream();

        ObjectOutputStream oos = new ObjectOutputStream(byteArrayOutputStream);
        oos.writeObject(instance);
        oos.close();

        return byteArrayOutputStream;
    }

    public static Singleton deserializeSingletonInstance(ByteArrayOutputStream byteArrayOutputStream) throws IOException, ClassNotFoundException {
        ByteArrayInputStream byteArrayInputStream = new ByteArrayInputStream(byteArrayOutputStream.toByteArray());

        ObjectInputStream ois = new ObjectInputStream(byteArrayInputStream);
        Singleton singleton = (Singleton) ois.readObject();
        ois.close();

        return singleton;
    }

    public static class Singleton implements Serializable {
        private static Singleton ourInstance;

        public static Singleton getInstance() {
            if (ourInstance == null) {
                ourInstance = new Singleton();
            }
            return ourInstance;
        }

        private Singleton() {
        }
    }
}