The Citadel/the Faith are SO getting destroyed in the grand finale of ASOIAF, magic has returned with Daenerys’s dragons and it’s all we need to know about the Catholic church’s fate.
This is not projection. GRRM clearly constructs the Faith of the Seven as an empty religion that does not produce any ‘miracles’, a direct contrast to religions based on naturalistic magic. A clear foil is established between the magic of the Valyrians/First Men/Drowned God/R’hllor vs the hollowness (anti-magic) of the Faith, which is upheld by the Hightowers. We are not meant to support GRRM’s version of the Catholic church (& its violent misogyny, but that’s a discussion for another day).
True. We aren't supposed to unironically or sincerely support any principle the Seven creates, develops, or endorses and it is the only religion in the entire known universe that has no "miracles" or magical ability to given/performed by any of its followers. I don't know if the institution and the religion itself will be destroyed. Because even if the Sistine Chapel or all the bishops, priests, nuns, etc. of our own world were mysteriously disappeared, there'd still be the worshippers and their memories and historical records of cathedra, Romanesque, etc. building plans, etc. Catholicsm would still exist, so the Faith and this miracle-less religion and the concept of the Seven gods themselves would exist of the Sept of Baelor and other important septs were obliterated. As for the Citadel (THE maester hub) and home to the grandest library of the Seven kingdoms, again, as long as people have their memory and some other records the maesters kept in various houses as well as copies of certain tomes, they can restore some measure of a "Citadel".
Now will there be some sort of destruction done against either the Citadel or the KL Sept? More than likely, esp since we still have all those casks of wildfyre Cersei is storing. If/when Dany ever makes it to KL and Westeros, she'll still have to contend with followers' anti-magicsm and xenophobia. And even if she becomes the Queen, most of the Seven Kingdoms, peasants and nobles, worship the Seven. A lot of villages have some sort of access to a small place of worship, if they don't already have designated spots. I don't think this religion will be eradicated anytime soon.