Are there any movies with binaural recording?

You've asked two different mutually exclusive questions. Binaural recording is one thing, using multiple microphones to enhance the sense of location is totally different. Binaural recordings use exactly two special microphones that are fitted inside a prosthetic head that is a life size replica of an average human head. The effect of a binaural recording only works when listened to with headphones - it doesn't work with any kind of speaker system, so it would be hard to sell a movie to theaters or home viewers that had binaural audio.

Then, there is the question of whether production sound (meaning the sound recorded while filming) might be recorded using multiple microphones used to create a sense of space, and the answer is that it's unlikely. Generally production sound is meant to capture dialog only as part of the acting. All other sounds are added later as digitally created effects, music, foley tracks, etc. Those other sound tracks that are not dialog are sometimes multi-miked to create a soundscape (an orchestral soundtrack is a very common example), but there's a very good reason why dialog is almost always mixed to a single mono track and then played back over the center channel speaker (or evenly split between left and right or left front and right front when there is no center channel).

When movies are distributed overseas, generally the dialog is replaced with a dub of the dialog in the language of the destination country. That means the dialog can't be completely mixed in with the other elements of the film, instead it is kept as a separate stem. This also enables DVD/digital/streaming releases to have multiple language tracks without having to have entire copies of the whole surround sound mix for each language.

If you did try to record all the sound elements of a film with multiple unidirectional mics in an array to replicate the speakers of, say, a 5.1 system, you'd quickly run into a huge number of problems. Right off the bat, you'd have to set the array up exactly the same way every time for every element that goes into the film or else when you try to mix them all together, it's going to be a huge mess. Second, you can't control the speaker placement of the final playback speakers, except perhaps in a THX theater, which means that the placement that you carefully recorded will be off when most people watch the movie. There are also huge audio engineering challenges with multi-mic setups, such as phase cancellation issues, and how are you going to set it up inside a car or bathroom or other small space? If you have some shots with the "spacial audio" and others without, the difference will be obvious and jarring.

The best overall solution for surround sound from both the aesthetic and business perspectives is the current one: separate elements are recorded in isolation, usually in mono or stereo, and then the elements are mixed into surround stems using surround panners and separate LFE feeds, while dialog is kept as a mono stem and fed to the center channel (which in a theater is behind the screen).