[Polycarp] departed this life, having always taught the things which he had learned from the apostles, and which the Church has handed down, and which alone are true . -ibid, 4
Again, the definition of “apostolic succession” is detailed as handing down that truth which was learned from apostles. Those teachings alone are true.
morden apostolic succesion:
The Eastern churches that are not in full communion with the Catholic Church celebrate the Eucharist with great love. “These Churches, although separated from us, yet possess true sacraments, above all - by apostolic succession - the priesthood and the Eucharist, whereby they are still joined to us in closest intimacy.” A certain communion in sacris, and so in the Eucharist, "given suitable circumstances and the approval of Church authority, is not merely possible but is encouraged. -Catechism CC-
Wherefore it is incumbent to obey the presbyters who are in the Church,—those who, as I have shown, possess the succession from the apostles; those who, together with the succession of the episcopate, have received the certain
gift of truth , according to the good pleasure of the Father. But [it is also incumbent] to hold in suspicion others who
depart from the primitive succession, and assemble themselves together in any place whatsoever, [looking upon them] either as heretics of perverse minds, or as schismatics puffed up and self-pleasing, or again as hypocrites, acting thus for the sake of lucre and vainglory. For all these have fallen from the truth. [Irenaeus Book IV, XXVI, 2]
terutilan agrees
in his writting He titles the of his anti-Marcion treatise,
The Prescription Against Heretics , as:
“None of the Heretics Claim Succession from the Apostles. **New Churches Still Apostolic, Because Their Faith is that Which the Apostles Taught and Handed Down **. The Heretics Challenged to Show Any Apostolic Credentials.”
we only see this shif later on
“And at the time of early dawn our Lord lifted up His hands, and laid them upon the heads of the eleven disciples, and gave to them the gift of the priesthood.”
[The Teaching of the Apostles] this 4th century , so it over a century after tertulian and nearly 2 centuries after igantius.
if there is no evidence of its existance , and the ones that do mention it have a diferent meaning
then theologicaly you can belive what ever you want , historically you cant this as truh unless you explain the lack of evidence and the diferent meanings for the same word used , and when they used the exact same words but didnt use the modern undestanding of it .
by showing sources of that time period , then now its historaclly sound.
until then the lack of evidence and the contradction of sources , shows otherwise ,