The most important featres of a library website in my humble opinion are as follows-

I would say just about the most important thing would be a search functions to search for items in the library catalogue. One of the main reasons people go to the library is to get access to the things in the library catalogues so a search function on a library website is very important.

Next I would say a section for address, contact details and also the social media platforms you can follow.

A section to explore the library, this should include things such as newly added books, materials and also an option to search via book category, bestsellers etc.

I also really like a section for 'recommendations' and 'books you must read'.

A calendar for upcoming events is a must. (Classes, events, etc.)

Something that I have found that would be really good on a library website would be a 'My Borrowing' section, this could include things such as books you have borrowed, fines, books on hold, this could also include books you have borrowed in the past, reminder of late or overdue books, messages for the library and so on.