I mean I read "What is Mathematical Analysis?" by Baylis and that was pretty cool, if a bit hard because you don't really come across analysis in school and it's a whole different way of thinking about mathematics. Really it depends on what kind of stuff you're looking for, and what kind of maths you think you'd enjoy recreationally at this point.
Pure maths in the context of University is not the same as your core modules or really your further pure modules either (these modules are more like the "methods" courses you see at University, which are definitely more on the applied side in general). But if you like thinking analytically and carefully, then pure maths is usually quite nice to look at.
But lots of people seem to look at books that introduce pure mathematics to A-Level students for the books they write about in their personal statement:
- A Concise Introduction to Pure Mathematics by Liebeck seems to be popular.
- How to think like a Mathematician wasn't that bad.
And as I said, the Baylis book I mentioned was the other one I read.
There's also "Reaching for Infinity" by Gibilisco which I haven't read, but I can assure you the material (that of discussing infinity rigorously) is quite accessible and in general just requires a solid understand of injective, surjective, and bijective functions. (Also it's just a really pretty area of pure maths for beginners imo, one of my favourite things I saw in first year.)
So you can look at some stuff there, and also the reading list provided by Cambridge and pick a couple of books that might tickle your fancy