I’ve read that the 4 councils (starting with Nicea) were convoked by the emperor, they are retained as an element of unity of the empire, with an authority superiorto the bishops and to the bishop of rome. Is this true?
Partially true, partially false.
The emperor did support bringing the bishops together in council to try to settle the Arian matter at Nicea. He had temporal reasons for doing so, the discord was causing civil strife in the empire. The Church had spiritual reasons for doing so, correct teaching and definition of doctrine.
The fact that the emperor supported the convening of the council, insisted upon it, is simply a fact. I guess I have to ask, “so what?”
The emperors did not have authority over the Church. A few tried to assert it, but one was even excommunicated for an evil massacre he perpetrated, and forced by the Pope to do public penance before he was allowed communion again.
In the East the emperor slowly gained control over the eastern bishops, though. It just didn’t happen with the Bishop of Rome.
The real weakening of Church power came during the rise of Despotism and Nationalism.
Emperors had no authority within the Church. They could call an Ecumenical Council, but they could not vote in one. They had no authority over doctrine.
The Church has certainly ceded authority to emperors in the past for various reasons. While the emerors had no authority as part of the divine constitution of the Church, it could certainly be provisionally delegated to them, even tacitly (as was the case in the times of the early Councils). Even until the 20th century, the emperor in the West was given a kind of veto power over papal elections (this was abolished by St. Pius X).