There is a chance to being a person venerated and suggested or recommended to being a saint, in which that person and all circumstances around that person are researched. The canonization process may take several years, but until that process is complete no person may claim that a single person is - without error or doubt - to being a saint. why? same reason we can’t or should not say someone is undoubtfully in hell. along with the simple fact of authority.
Eastern Catholics do not include all Greek Orthodox Churches. which is why I stated there may be some differences from a certain date IF they still acknowledge the canonization process in some form. However, Eastern Catholic churches refers to communities/churches in commune with the Catholic Church as a whole.
Therefore, in all likelihood, the Saints or people proclaimed as Saints within an Eastern Church is indeed a Saint for the entire Church of Catholicism. Its just that most people have a closer connection to Saints closer to home. so you might not hear about those from Eastern Europe or Asia, while hearing more about Saints from western europe or the americas