Tobias Forge has gone on record saying that Copia must prove himself first in order to ascend to the level of Papa.
Copia became Papa IV in March 2020.
Cardinal Copia is an illegitimate child of either Papa Nihil or Papa I.
Papa Nihil eventually relented on his taking over, despite his complaint that only his bloodline should lead, and Copia has the same heterochromia of all the Papas. So...son or grandson he hadn't acknowledged at that point.
Cardi C's appearance does seem to bear some resemblance to Papa II. Specifically, when he isn't in stage attire and without his skull paint.
The "Kiss the Go-Goat" video drops a huge hint that Imperator was pregnant with Nihil's child when she left him, so it's very likely that this child grew up to be Copia.