“...and papacy is seen as prefigured in Aaron.”
Where do you see that, Alex? +Clement doesn’t say that. No Father does.
There is no short prooftext of that, however, the logic of the letter is that the Church Catholic is likened to the priestly system established by Moses, and in the priestly system of Moses there was a chief priest Aaron. The call is then made to submit to that system and avoid the sedition.