"Greek" pederastic relationships were a general Indo-European custom, related to the warrior function. They served for youths and men o initiate teenagers into the world of men - in a way it was very similar to, say, initiatory rituals among Pacific peoples and so on. It is just that Greeks and Romans were the only ones to talk about it openly - Germanics are documented as having done it (see what Ammianus Marcellinus 31.9.5 has to say about the Taifali) and Celts almost certainly did it too - see Cuchulainn's relationship with Ferdiad for a good example. Do not let Christians scribes passing in silence over it convince you that it was not a thing.

These relationships continued on in Europe, the church neither recording them nor punishing them. Where there is a record of them, you learn that as much as a third of the male population in this or that Italian city had one such relationship, per example - these are numbers known from the criminal records, and again, the church did not care that much. These mostly happened among guild members, worksman forces, etc, and there is a variety of reasons the boys did it: gifts, affection where it was lacking elsewhere (no girls till you get married mister), apprenticeships, favors, etc. There is a record I remember, per example, of boy worker who outraged whatever guild master because their princely lover had given them better shoes than the master himself, per example - a bad omen, because the working population did not worry about such accusations, whereas the nobility very much did.

A thing worth noting is that this remained an urban phenomenon; in the country, deviancy took other forms, like incest, covering up of rapes, bestiality specially, etc.

They most certainly were not continued "in the Catholic Church", though such relationships did happen there because of course lol, they happened in most places. In some places, homosexuality (sodomy) was not condemned because it would be awkward since the local clergymen were known to be engaged in such things too - in any case the Church was still most certainly not the place where this most happened, lesbian nuns were more common. Pederasty, in the medieval and early modern period, was a working populace phenomenon, and amid the nobility. The bastard son of Louis XIV, Louis de Bourbon, had an affair, when he was very young, with Philippe of Lorraine, a knight who belonged to La Sainte Congregation des Glorieux Pédérastes ("Holy Congregation of Glorious Pederasts", what a name), a secret society of libertine deviants a la Marquis de Sade (many such things). This very much humiliated his father and led to the young lad to die at 16 after catching a disease in combat, which he did to get his father's affection back. Philippe of Lorraine was himself an eromenos as a youth and was painted as Ganymede no less, look it up. It was a more serious offense to the reputation of a noble, though amusingly here we could tongue-in-cheekly say that this resembles very ancient warrior pederasty more, teehee.

If you want to learn more about this, pick, tbh , any book on historical homosexuality: the truth is, pederasty is not limited by "age" as we think of it - eromenos could be full grown youths in their 20s or early pubescent boys - and almost all expression of male same sex desire historically attested took on these forms, in the Indo-Euro world, and in different forms but equally age-bracketed ways in Africa, China, the Muslim world, etc.