This is one of those books were trying to take any kind of stance about the interpretation is very fraught and intimidating, so I'll just comment on a kind of marginal thought I kept having, especially in the last ~50 or so pages that are packed with all those revelations: Is any of this obliquely talking about hallucinogens? My spurious and inadequate evidence:
time loop / ouroboros imagery felt a lot like how you experience time while tripping, getting caught in a train of thought that leads to its own beginning and then realizing you're not even in the first cycle, marveling at the deja vu and having a vertigo / looking into facing mirrors feeling. For me at least, that describes both acid and thinking to much about citadel of the autarch
feeling like the path you're walking (figuratively and literally) is getting cemented into time and that you're tracing some kind of ball of yarn behind you that is invisible but not at all ephemeral, with little bookmarks along the path that you come back to in your mind and see in new ways in the context of the full journey. again, to me that description works equally well for walking through the park on acid or mushrooms and for piecing together the mix of puzzle box and mystical elements of book of the new sun
This might be nothing, or maybe I just think about memory a lot while tripping and that happens to be the most blatant and obvious theme of the book. Or maybe gene wolfe was a crypto hippie, who's to say
Is this your first read-through of BotNS? I do think this is a very compelling interpretation. That being said, I do know that Gene Wolfe has strongly pushed against "you must have been so hiiiiigh writing this man" in interviews, but I think that's out of frustration for interviewers asking lazy questions. But even though he's this arch-catholic conservative, I figure that he's such a product of the 1970's SF convention scene that its not impossible for him to intentionally bring psychadelia into his writing.
First read through and first Wolfe, and I don't really have a sense of the landscape of conversation around the book. The comparison felt strong to me in CotA, but whether that was part of his intention sounds a lot less likely--also, I realize you don't have to be even a little like PKD for writing speculative fiction about time and memory to incidentally sound a bit psychedelic