Just as the saints of the Roman Church are recognized as genuine saints throughout the entire Catholic Church, so too the saints of the Eastern Churches are recognized as genuine saints throughout the entire Catholic Church. The different particular Churches simply venerate their own saints. For example, the Churches of the Byzantine tradition may not liturgically venerate someone like St. Ignatius of Loyola. That doesn’t make him any less of a saint. Similarly, just because the Roman Church does not venerate St. Gregory Palamas as a saint (like many/most of the Churches in the Byzantine tradition do), that does not make him any less of a saint.
Bear in mind that one of the “Doctors of the Church,” St. Gregory Narek, belonged to a particular Church that was not in communion with the Church of Rome during his lifetime. But he has been venerated as a saint by the, I believe, Armenian Catholic Church since it was received into communion with the Roman Church.