The current public link button on each notebook points to a lowercase version of the username. The paws-public.wmflabs.org/paws-public/ endpoint, however, will throw a 404 for users that have an uppercase letter that is not the first letter.
For example, my ChicoBot account can have its notebooks accessed via http://paws-public.wmflabs.org/paws-public/User:chicoBot/ or http://paws-public.wmflabs.org/paws-public/User:ChicoBot/ . The button, however, points to http://paws-public.wmflabs.org/paws-public/User:chicobot/ which is not found.