Literal.club is probably my favourite. Cleanest interface of anything I’ve tried, and a really great API to use if you’re a developer. It also recommends profiles with a similar taste to yours, which can be helpful for discovering new books.
Edit: I looked into Bookwyrm and it turns out you can get book lists (e.g. currently reading) as JSON. For example, bookwyrm.social/user/mouse/books/reading.json. For anyone who wants an API, this might be enough.
Unfortunately :(