Actually, that's more junk logic on JPII's part. The Pope is the guardian of the deposit of faith. First and foremost,not the servant of Unity. He's imbibing in his phenomenological gobbledygook that amused Chesterton so much. (See Chapter 8 of Thomas Aquinas: The reference that Aquinas was willing to call eggs, eggs and not chickens "becoming".) JPII keeps yapping about the essentials of the mission but he doesn't understand the nature of the papacy in his writing. And finally, error plus truth is still error. Double talk doesn't make him orthodox in his statement. It falls right into the double part of Catholic and Rationalist that St. Pius X condemned.
From this text it is clear that by the will and command of God the Church rests upon St. Peter, just as a building rests on its foundation. Now the proper nature of a foundation is to be a principle of cohesion for the various parts of the building. It must be the necessary condition of stability and strength. Remove it and the whole building falls. It is consequently the office of St. Peter to support the Church, and to guard it in all its strength and indestructible unity. (Leo XIII, Satis Cognitum)
In order, then, that the episcopal office should be one and undivided and that, by the union of the clergy, the whole multitude of believers should be held together in the unity of faith and communion, he set blessed Peter over the rest of the apostles and instituted in him the permanent principle of both unities and their visible foundation. (First Vatican, Pastor Aeternus)
The Council gives the reason for the primacy: guarding the unity of faith and the unity of communion. So much for the Pope not being a servant of unity. Moreover,
But the blessed Cyprian . . . among other things, says the following: "The beginning starts from unity, and the primacy is given to Peter, so that the Church and the chair of Christ may be shown (to be) one: and they are all shepherds, but the flock, which is fed by the Apostles in unanimous agreement, is shown to be one." (Pope Pelagius II, Letter to the Schismatic Bishops of Istria, 585 AD)
It falls right into the double part of Catholic and Rationalist that St. Pius X condemned.
I suppose you are citing the part of Pascendi (§18) where he condemns how the Modernists would say one thing in their homilies, and another in their 'scientific' writing? But this is not applicable, since UUS is a single document.