Why does Academy call their best film a "picture"?

Because if they give away prize for "moving picture" the home movers would win every year.

The "picture" is a neologism. A neologism that is actually old. Picture in context of a film is derived from the same thinking as "movie". Because "Moving pictures". Each frame is a picture that when set in motion creates the illusion of movement. The moving is from the action machine and celluloid take rather then effect is create.

And until last 20 years movie was a set of still pictures set in motion by a machine in the projection room.

With the introduction of digital copies there is no picture whatsoever. But because Academy don't see the point of creating two categories for "pictures" and "digits" (because some movies were filmed digitally and then transferred to film and vice-versa) and they assume that people will understand that "best picture" awarded by Academy of Motion Picture Arts and Sciences is not about oil painting they don't see a reason to change a name.

Just like a smartwatch is a watch no more but is still called a watch but you don't watch it anymore because you look data on your smartphone.

Consider this a Speculative Answer Based on Putting Some Historic Things Together:

As you have mentioned, The Academy Awards are voted upon by members of The Academy of MOTION PICTURES Arts & Sciences, which was founded in 1927.

Motion Pictures WAS popular and accepted termonology used, because it specifically refered to the invention of The Motion Picture Camera, which was invented roughly 50 years earlier during the 1880's.

The cinema of the United States, often metonymously referred to as Hollywood, has had a profound effect on the film industry in general since the early 20th century. The dominant style of American cinema is classical Hollywood cinema, which developed from 1917 to 1960 and characterizes most films made there to this day. While Frenchmen Auguste and Louis Lumière are generally credited with the birth of modern cinema,[7] American cinema quickly came to be the most dominant force in the industry as it emerged. Since the 1920s, the film industry of the United States has had higher annual grosses than any other country's. https://en.wikipedia.org/wiki/Cinema_of_the_United_States

The Academy of Motion Pictures was concieved by MGM head, Louis B. Mayer (MGM founded in 1924) and thus there is also an association with the birth of Hollywood (American Cinema "A Birth of a Nation" @ 1915+) and the concept of "Film Studios": Industry with companies owning & distrubuting motion pictures. Basically turning motion pictures into a profitable business and creating "brands". One may argue that creating the Academy was a way to "dominate" and "market" America Cinema to wipe out it's European counterparts. Basically, America was a better salesman and/or that the popularity of the term "motion picture" helped to win it out!

A film, also called a movie, motion picture, theatrical film, or photoplay, is a series of still images that, when shown on a screen, create the illusion of moving images. (See the glossary of motion picture terms.)...

The name "film" originates from the fact that photographic film (also called film stock) has historically been the medium for recording and displaying motion pictures. Many other terms exist for an individual motion-picture, including picture, picture show, moving picture, photoplay, and flick. The most common term in the United States is movie, while in Europe film is preferred. Common terms for the field in general include the big screen, the silver screen, the movies, and cinema; the last of these is commonly used, as an overarching term, in scholarly texts and critical essays. In early years, the word sheet was sometimes used instead of screen. https://en.wikipedia.org/wiki/Film

I'm not sure if your question is really more centered around the abbreviation choice and/or WHY the termonology has not "updated" to suit the temronology of a modern audience, but my assumption, despite whatever quams one my have with the history of the Academy and/or it's current film and category choices, seems to go back to part of it's own original name: "Arts and Sciences", which means, it is about PRESERVING the origins of "motion pictures" (and North America's domination of it) being the most common termonology used at the time of it's creation.

As mentioned in the Wikipedia article above the word "film" comes from Photographic Film/Film stock and although the first photgraphic process (the daguerreotype), was first concieved in 1839 before the term "motion picture" and/or the creation of motion picture cameras, the wikipedia article has it worded in such a way, where is seems "Film" (photagrpahy) was the [most popular] MEDIUM of showing "motion pictures" and "motion picture" was thought of to be a "type" of filming/photagrpahy.

In addition (also stated in wiki article) a "picture" in the context of Motion Picture still referes to an image, but rather it donates a series of images--and therefor is not a falsehood. It's just that a series of images may be different than another series and so one has to find a way to "label" them into single groups of "something". A Motion Picture is a series of images or collected into "a moving image".

It all seems to be a historic & cultural matter of semantics in being able to better determine what lingo and "patent" would work and stick vs why others did not.