Plural bishops does not necessarily mean there wasn’t a monarchical rule. From the earliest times down to the present dioceses have had auxiliary bishops.
The tradition in the Liber Pontificalis was that Peter appointed three episcopoi (Linus, Cletus, and Clement) over the Church of Rome to perform the sacraments and fulfill the priestly offices while he preached and taught. I’m sure there was no confusion about who the head of the Roman Church was while he lived though.
My Church in Ohio had Church Elders, but I don’t know all the functions they did.
I assumed they were the ones that made the church ready for the Priest each service since I always saw them unlocking the doors, filling pamphlets, and stocking candles.
Before 300 ad ...only the "bishops " would administer the eucharist ... when the church came to believe the mass was a sacrifice they began to have "priests" to offer the sacrifices
The tradition in the Liber Pontificalis
There is no evidence that Peter was even ever in Rome ...