I'd be interested to hear more! My other book clubs very often share a list of similar books and that's something I've never thought about trying to do here but would be cool.
None of the books/authors I'm about to recommend are similar to this one, hopefully you don't mind.
Haruki Murakami of course must be mentioned, like you said. For anyone who hasn't read him,
Kafka on the Shore is probably the easiest/most engaging place to start.
Sakaya Murata is a big one in contemporary Japanese literature, she's most known for
Convenience Store Woman and that's what I'd recommend as well (I think she only has one other book translated into English at the moment, but I didn't enjoy that one as much). She writes a lot about challenging taboos, conformity, and the pressures that society puts on single women. The writing style is kind of dry and similar to Kawaguchi's, but I'd argue that it's more intentionally done to drive home her points. There's also a healthy dose of the "something here isn't quite right" that you get in a lot of Haruki Murakami as well.
The Factory by Hiroko Oyamada is another one I really liked. This is a Kafkaesque novella about three people who work in a gigantic factory. What does the factory make? Unknown. What are their jobs? Unclear. It's honestly pretty tough to describe this one, but if you're intrigued at all, I recommend it. My one caveat is that for
@Violentvixen in particular and anyone else who sometimes has trouble following books with multiple narrators, this book may be a little challenging in that regard. But I think that's part of the point.
Scattered All Over the Earth by Yoko Tawada -- I'll be honest, I read this a few years ago and I don't remember it super well, but I thought the concept was interesting enough to mention: in the near future, after Japan is wiped from the face of the earth (and the memories of most people) in an unspecified climate disaster, a woman who was born there now speaks her own invented language and travels around looking for anyone who can still speak Japanese. Apparently it's the first book of a trilogy, though I haven't heard anything about the other books being translated yet.