How similar is the show to the Hannibal films in terms of plot?

Both very similar and not at all similar. Some characters are gender flipped and that changes the course of their story. Some characters are blended together (Will is a mixture of Will and Clarice from the books/movies). Some characters say lines spoken by different characters in the books under different circumstances. Some plot points are the same, but take a very different route to get there. It's basically Bryan Fuller's slash fanfiction of the Hannibal books, and he gives us delightful call backs to the source material.

The second half of Season 3 (Red Dragon Arc) is really the only thing that bears true resemblance to any of the films. The rest of it is kind of, like, what the Shape of Water is to Creature from the Black Lagoon. It carries the same, recognizable core DNA as a launching point but the themes and stylistic choices are pretty different. And, like Shape of Water, it’s also a love story :)

The third season of the show follows the book ( and the movies) Red Dragon very closely BUT with a very rehashed context.

The first two season is original content which imagines the prequel of Red Dragon. It borrows themes, events and characters from the book.

Tbh the only arc that follows a linear plot to the novels is the Red Dragon arc and part of the Verger arc. The show takes bits and pieces of each of the novels and characters and spreads them out throughout different characters in shows. Sometimes it’s intentional as part of Bryan’s vision and other times to avoid copyright. But overall, the show is incredibly original in its adaption of the Hannibal lore and better for it. It really brought Hannibal to the modern day in perfection.

It's different but there are certain things that reflect the films/books more than others. I'd say they're more like Easter eggs.

The show is very much about Hannibal and Wills relationship and character arcs, which is not what the films are at all.