Priests in the Byzantine are permitted to remain married, if they were married before ordination.
Only inside their “traditional” areas. It’s not allowed in the US, Canada, Australia, etc., where the majority of Byzantine Rite Catholics live. Much of the OCA is made up of former Byzantine Catholics who decried the violation of their communal agreement with Rome when Rome decided to ignore its side of the bargain in allowing married priests.
The various liturgies were also Latinized and are not the originals written by Sts. Basil and Chrysostom and used by the Orthodox Church. The differences amount to a couple of words, but they are extremely important theologically.