Does the EOC have a set of universal daily readings or prayers, or anything to that effect (something like the Divine Office/Liturgy of the Hours in Catholicism)?
We have a daily office as well. For the "hours", pretty much the only thing that changes are the "collects". For vespers, there are more propers and, if one does them, there are different chunks of the psalter on each day. Only on feasts are there readings at vespers. Compline has significant variation depending on the practice of the place, it can become a dumping ground for extra material. Midnight office differs by weekend vs weekday. Matins is complicated since it's like 4 services stapled together with significant variation. Essentially, without a pile of extra books, you can do the hours, the midnight office, and compline (by some practices). For more than that, it gets involved.
Sometimes I wish it were as easy to get more parts of that as it is to get what I receive on an app for the "daily readings" - which includes the Gospel and the Epistle reading for the day, information about major Saints or feast days, including the Apolytikon and Kontakion.
I enjoy when we have a Matins service and there is more to be learned.
they are not daily prayers officially, but I know folks and/or parishes who make canons or akathists as part of their regular prayer routine. as an example, while in college, we would do the Akathist to our Sweetest Lord Jesus Christ every Monday in Church.
I'm not looking to add to my prayer rule, which is really fairly simple. But I enjoy reading the rest because that's where I've learned so many things I wouldn't have known even to ask about otherwise.