That would be both Greek Orthodox and Greek Cathoilics
It's interesting, though---Constantine XI died in full communion with Rome. So it is possible to be a saint in Orthodoxy while being in communion with Rome post-schism?
I don't think he is an official saint. He certainly died a heroic death and many do venerate him as a saint, but I don't think he has feast day or was ever glorified. Correct me if I'm wrong.
Perhaps. Does anyone know who Emperor Constantine the New, venerated on the Greek calendar on Sept 3/16 is?
And no. Constantine XI who was willing to sell out the Faith for a kingdom of this world is not remembered by the Church as a saint.