I worked in an NHS medical library & did a L3 diploma. I checked in and out book loans & signing up new users, but a large part of my time was spent troubleshooting IT issues.
After some training from a qualified librarian I showed people how to search for and access research articles, manage references, and eventually conduct literature searches. I also sourced copies of research articles and book chapters for colleagues across our Trust to support ongoing study and professional development.
Sometimes I helped people navigate new systems, like a pull printing system, the ebook library or a new way of making mileage claims. I also processed new books and disposals.
In a public library I'd imagine you'd get a lot of enquiries for help with using computers - job searches, online forms, benefit applications - and probably support some people with v limited IT skills.
I'd expect you'd need to demonstrate good IT skills (MS Office type stuff) in application & at interview.
I found it quite difficult to move between sectors - despite a couple of years experience I couldn't even get shortlisted for academic library assistant roles (I got interviews for general admin roles at the same institutions, so I don't think my application style was the issue).