It has various opt-in things that log stuff like crashes that may have personal information. It also uses some client-server type apps that may not deliberately identify you, but do contain “asked locations of adult bookshops”, “asked for directions to the #3 most popular one (hey should we give that a rank boost?)”, as well as “wants to know the weather in Montana”.
If you use iCloud backup they have a backup, I’m fairly sure it is encrypted so they can’t get at the contents, but they do have the size & rate of change.
If you opt-into iCloud Keychain sharing and don’t use apple’s key escrow they can’t read that, but the can do finer grained traffic analysis. If you do have them escrow the keys they probably can’t read them, depending on how secure the HSM they use really is & if the write their little HSM management app thing correctly.
However I’m sure they don’t record anything on purpose that people would object to. …however it is way easy to price little fragments of information back into something people consider creepy.
