Try A Canticle for Leibowitz
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I've heard the Silo books go a similar direction. I've not yet read them; they're on my short list though
I believe Silo is (or is based on) the Wool books.
Silo is the name of the full series of books. It started with a short story called Wool.
TIL 😉
Ah, TIL indeed. Do you recommend starting with the short story? Or just diving into the main novels?
The short story is the first part of the first book, also called wool, so you can do both at the same time !
It’s kind of confusing at first, but the first two books in the 3-book Silo series were originally released as short stories that were eventually combined into “omnibus” editions. So if you want to read the trilogy (which you should, they’re great) you want to read Wool omnibus, Shift omnibus, and Dust. If each book you’re looking at is ~500 pages, you’ve got the right one.
City of Ember comes to mind
So bit of a stretch recommendation but I can never turn down a chance to recommend this author.
If you like the general idea of an author exploring what-if premise of people living (like how the Fallout vaults are given specific scenarios to live in), you might like Ted Chiang's short stories. For example, "Hell is the Absence of God" explores what life might be like if angels (heaven and hell) were real but come into societies like tornadoes or hurricanes due to their supernatural power (think tornado chasers). There's world building in it to realistically support the premise of the story (e.g. support groups for those affected) and is generally really thoughtful.
Again, very much a stretch to Fallout vaults, but really deserving of a read if you are more interested into exploring the realism in a world built around certain premises.
Tangentially related, but you might enjoy Margaret Atwood's Year of the Flood trilogy.
Lucifer's Hammer is very good and somewhat related.