I invite you to read this previous content report.

I would reiterate that the billing block on a movie's poster is laid out contractually. Agents and studios negotiate the placement of each name, the order, etc. While I understand that the film's "official website" theoretically carries some merit, I would also say that landing page used in the other content report looks quite generic, and I would be quite skeptical that it is being presented with the same kind of legal significance as the billing block on the poster. Note again that the colon does not appear on the poster anywhere, either in the title treatment or in the billing block.

If you go to this page on the Disney-owned Hulu and scroll down, you should see Die Hard With a Vengeance in the related movies section at the bottom, with no colon. https://www.hulu.com/movie/live-free-or-die-hard-9b712adb-7875-4462-a3d9-9f5429c9fef6

As Disney is now the copyright holder for the Die Hard movies, following its acquisition of Fox, this would surely be at least equally relevant in deciding what the title is as the other website. Same if you go here -- the page will redirect to a signup page, but you should briefly see the title of the film appear in your web browser's display name, without a colon. https://www.disneyplus.com/movies/die-hard-with-a-vengeance/7PTXoHqR8mCE

Although the subsequent movies in the series have the phrase "Die Hard" at the end, I think it is also safe to observe that the third, fourth, and fifth Die Hard movies all have phrases as titles: Die Hard With a Vengeance, Live Free or Die Hard, and A Good Day to Die Hard. I find the idea that the title has to appear intact on screen very weird; I do not think the logical leap would have been made to add colons to those titles had the title designers chosen to split them up, because Live Free or: Die Hard and A Good Day to: Die Hard do not make much sense (and frankly, I don't think Die Hard: With a Vengeance makes that much sense either, compared to, for example, Die Hard...With a Vengeance or Die Hard -- With A Vengeance).

As a last argument here, I quite coincidentally had a friend over and we watched Strange Brew, the Bob and Doug McKenzie movie. On screen, within the film, the title is The Adventures of Bob and Doug McKenzie (credit disappears) (beat) Strange Brew. However, the billing block on the Blu-ray simply says Strange Brew, which is what it is on the site, and what I think most people recognize as the title of the movie.