Harvard referencing bibliography - must the year be in brackets?
As far as I know, the term Harvard referencing is usually a synonym for the author–date parenthetical referencing in general, similar to how Vancouver refer to numerical style of reference. I am not aware of an authoritative manual for Harvard style that is analogous to Chicago or APA. It is possible that different organisations use the term Harvard for their own author–date styles.
Different author–date styles differs on how citations and the reference list are formatted. For example, according to the Chicago Manual of Style, the reference entry for a book look like this:

Lastname, Firstname, and Lastname, Firstname. 2020. Title of book. Place: Publisher.

while in the 7th edition of APA it looks like this:

Lastname, I., &amp; Lastname, I. (2020). Title of the book. Publisher.

These two are perhaps the better known author–date styles, but there are many different variations used by different publications or organisations. The Zotero Style Repository currently lists over 4,000 different author–date styles. (Maybe your institution style is already listed there.)
If you are required to precisely follow your university style, then the only &quot;correct&quot; format is what the style prescribes. (For a university coursework, many instructors might be satisfied with a close approximation. You might want to check whether the (possibly 6th edition) APA format suffices for your need; it should be included in any reference generation tools.)