Though further to the above Eusebius does mention the Papacy, although he doesn’t seem the biggest fan, as some people in the East later started to rebel, though he does at least acknowledge the authority
“And when a dissension arose about these said people [the Montanists], the brethren in Gaul once more . . . [sent letters] to the brethren in Asia and Phrygia and, moreover to Eleutherius, who was then [A.D. 175] bishop of the Romans, negotiating for the peace of the churches” (Eusebius, Church History 5:3:4 [A.D. 312])
“And the same martyrs too commended Irenaeus, already at that time [A.D. 175] a presbyter of the community of Lyons, to the said bishop of Rome, rendering abundant testimony to the man, as the following expressions show: ‘Once more and always we pray that you may rejoice in God, Pope Eleutherius. This letter we have charged our brother and companion Irenaeus to convey to you, and we beg you to receive him as zealous for the covenant of Christ’” (Church History, 5:4:1–2).
“A question of no small importance arose at that time [A.D. 190]. For the parishes of all Asia [Minor], as from an older tradition held that the fourteenth day of the moon, on which the Jews were commanded to sacrifice the lamb, should be observed as the feast of the Savior’s Passover. . . . But it was not the custom of the churches in the rest of the world . . . as they observed the practice which, from apostolic tradition, has prevailed to the present time, of terminating the fast [of Lent] on no other day than on that of the resurrection of the Savior [Sunday]. Synods and assemblies of bishops were held on this account, and all, with one consent, through mutual correspondence drew up an ecclesiastical decree that the mystery of the resurrection of the Lord should be celebrated on no other but the Lord’s day and that we should observe the close of the paschal fast on this day only. . . . Thereupon [Pope] Victor, who presided over the church at Rome, immediately attempted to cut off from the community the parishes of all Asia [Minor], with the churches that agreed with them, as heterodox. And he wrote letters and declared all the brethren there wholly excommunicate. But this did not please all the bishops, and they besought him to consider the things of peace and of neighborly unity and love. . . . [Irenaeus] fittingly admonishes Victor that he should not cut off whole churches of God which observed the tradition of an ancient custom” (Church History 5:23:1–24:11).
“Thus then did Irenaeus entreat and negotiate [with Pope Victor] on behalf of the peace of the churches—[Irenaeus being] a man well-named, for he was a peacemaker both in name and character. And he corresponded by letter not only with Victor, but also with very many and various rulers of churches” (Church History, 24:18).