How do I search for a movie on the Apple TV website?

On the Apple TV website tv.apple.com, you have access to the Apple TV+ content from the subscription of the same name. You do not have access to much larger catalog of iTunes Store movies (buy or rent) on the site.

There is currently no text search on the site. Everything that is available through the site, is presented on the home page. Note that each row is scrollable horizontally to reveal more content.

On Macs with macOS Catalina 10.15 or later, you would be redirected to watch in the TV app instead. The TV app does offer access to more content, namely the iTunes Store and other Apple TV app channels, and text search.

Are you referring to www.apple.com/tv? If you are then this site is not a site for searching for movies. If you are not referring to that website what site are you referring to?