I’ve had feedback from customers that they could not book more than 4 weeks in advance – is that correct, or is that just while I’m still on my trial period?
Yes, correct. Customers cannot book classes more than 4 weeks in advance by default.
This is setting you can change on Settings > Main Settings

Note that you can also create courses (Eg. 8 Weeks Course) where customers prepay the whole course and are automatically booked into every class in advance.