Apologies in advance because I don't have much on this, as I more remember me reading the story than the actual story. In any case:
It concerns a girl, living with some older relative. There is definitely a house (they're living in the countryside or maybe though less likely suburbia, but certainly not in a bustling city). The girl, as best I can recall, is living with an older female relative (I think her grandmother), though I'm unsure whether it's just the two of them. There are also cats, which are significant to the story progression. I think the girl could also talk to or telepathically communicate with the cats. There may or may not be further magic involved (if there is, it definitely has to do with the cats), but I am unsure about this as I read it a long time ago on the same summer vacation I read Narnia, Nils Holgersson, Harry Potter, and a bunch of other fiction with young protagonists, so I might be mixing some details up. Cats, house, and older female relative were definitely unique to this one, though.
What I can recall very vividly is that the story had a very cozy feel, in a way that the other books, including Narnia and Harry Potter did not. The universe was also much more constrained than those other two. I read it in German, but I am unsure whether it's originally in German (I was reading almost everything in German at that age). This was all in the early 2000's, so the story is not newer than that, though it might be a lot older. I don't remember any technology in the house, but my guess is it's late 20th century literature (both in origin and setting).
Things which I thought of and which tick some of the boxes but are definitely not this story, include: Coraline, Pippi Longstocking.
Sorry about the sparse details again, I'd appreciate any suggestions!