I’m baptized Protestant, chrismated Romanian Byzantine; my father used to be Roman Catholic but left before I was born. What rite am I part of?
1990 Code of Canons for Oriental Churches:
Baptized non-Catholics coming into full communion with the Catholic Church should retain and practice their own rite everywhere in the world and should observe it as much as humanly possible. Thus, they are to be enrolled in the Church sui iuris of the same rite with due regard for the right of approaching the Apostolic See in special cases of persons, communities, or regions (canon 35).
Baptized Protestants who become Catholic are automatically enrolled as Latin Catholics, regardless of what Church receives them into the Catholic Church. That would mean that you are enrolled as a Latin Catholic due to your Protestant baptism. You do have the right to petition to be enrolled in the Romanian Greek Catholic Church.