from a legal standpoint, you do need to contact to the publisher or the author to avoid any chance of being sued or your video being demonetised. using said image with no artistic intent (e.g; if it's a stock photo of the book cover) then you have a chance of the video being removed or requested to be removed by the publisher or author, as seen on a lot of book review blogs. the chance is so tiny, though, as most publishers do not actively look for copyright infringement in terms of book covers, and many do not bother to copyright their book covers as works owned by them.
in terms of fair use, the discussion about the book isn't about the cover, so that isn't relevant. like i said, any artistic development with the book cover (for example, the book, a mug of coffee and a vase of flowers) would count as fair use of the book cover if you were terrified of the tiny minuscule chance of such an event happening. a blog my friend runs doesn't feature a book as the "book of the season" unless the author or publisher replies and allows it to be featured, and a lack of reply also counts (to them at least) as a non acceptance to the sharing of the cover.
tl;dr: the chance is tiny for you to be sued, but legally you are in the wrong
