After discovering a prominent fan restoration project, I'm thoroughly confused what the original aspect ratio is. Is the picture on DVD and blu-ray matted out and how all eight films differ? Are there open matte releases of the series on streaming services (the restoration project maintainer claims that there are on Amazon)?
The original theatrical releases are the definitive ones; digital releases in different ratios are common but are not usually what the director intended.
The original theatrical releases in cinemas are usually considered as the intended format for the movie. However the original version is recorded and distributed, each scene is (usually) carefully composed to work in a particular aspect ratio (and this usually stays the same for the whole movie unless you are Wes Anderson who used at least three different ratios for The Grand Budapest Hotel). Movies are edited for particular effects and the aspect ratio is part of that effect. Whatever the original digital or film camera records is irrelevant as the version this source is edited into is what the director wanted audiences to see (including plenty of messing about with colour and special effects added in post production).
But many sources (especially early DVDs) don't respect this. Many broadcasters and distributors who expected the movie to be watched on TVs thought audiences would react badly to wide aspect ratios (which leave large amounts of black space above and below the content) when fitted into a normal 4:3 TV screen. This has to be achieved by re-editing the movie in various ways (pan and scan was once common where an editor tries to capture the interesting parts of a wider picture by varying the part shown horizontally; other versions simply crop out the edges of the wider picture without any horizontal movement).
Needless to say this is a horrible abomination and should not be done (not least because modern TVs allow the idiot viewer tho choose this sort of horrible effect without affecting any other viewers' ability to get the originally intended ratio).
With a wide proliferation of different forms of distribution it is hard to be precise about which versions of the Harry Potter movies have been distributed digitally. But they were all originally released in 2.39:1 ratio widescreen cinema formats (whether shown digitally, from film or even in 3D). Some digital releases are different (the Amazon versions, for example, are in 1.78:1) but this is not the intended framing for the movies and will be inferior to the directors' intents. Some DVD, BlueRay and online versions do respect the original aspect ratio so you don't have to put up with the inferior versions from Amazon if you don't want to.
And that video "restoration" project is horrible. You can clearly see more of the scenes in the original ratio and less in the 1.78:1 versions.
Your question is difficult to answer. Why? Since it "lumps" all eight films into one "pot" when all of them were filmed over a 10 year period (2001 - 2010/11) by six different cinematographers. Each of these artists in film have their own "choice" camera model & lense aspect ratio preference.(See more below).
The question to ask first then is which of these eight films was filmed digitally using a digital camera for an audience that could watch these movies on their home entertainment system in high definition vs. earlier opted to go to a movie theater to see the release in Panavision on film reel and then examine an American/World audience from 1970-2003 who predominantly owned a television set with 240-360p with a 4:3 Television "box" aspect ratio vs. what the movie theater had - a panavision wide screen..then proceed from 2001 through 2015 to household televisions around the world shifting/moving to High Definition television.
All this occurs during while these films were made from 480p..to 720p to 1080p ..higher and higher definition available on your television in your home..and a move away from going the the cinema to see these films. This aspect ratio shift from 4:3 to 16:9 available on TV's and in DVD player/recorders, and how DVD's also had to be modified from single to double to high density to Blu-Ray over this same time period. DVD's that developed to hold both image quality and Dolby high definition sound which never had to happen on your 1980s era 4:3 TV but happened all the time on the cinema screen. So you have to examine this phenomenon of six different cinematographers each w/their own choice of camera and aspect ratio, and Warner Bros who distributed all 8 films who want to get it into the hands of the widest viewership possible--
To keep the answer short let's simply examine the first two films - The first 2 movies were both directed by Chris Columbus one year apart (Seale & Pratt Cinematographers). Both were much better High Definition in pan-scan (1999 Millenium XL 35MM 4:3) than the 3rd Harry Potter Movie, filmed two years later (2004, directed by Alfonso Cuaron, cinematographer M. Serensin) Chris Columbus and both cinematographers preferred Super 35, which films a 35mm 4:3 frame which is then cropped at the top and bottom for theatrical release. Alfonso Cuaron used Panavision, which is a 35mm 4:3 frame but with 2004 technology shifting the camera to digital (Digital Video Genesis) which uses an anamorphic optical lens to "squash" what is being filmed at the theatrical aspect ratio.
What all this means is, you've missed the war that went on between the 35MM camera folks who developed film in a higher resolution in a dark room vs. going digital with less resolution but everything could be edited / done on a computer. It also means that there is actually more image available above and below the theatrical frame for use in the first two movies so they look much better than the 3rd one filmed digitally. The first 2 films actually show "more" movie than the 3rd one on 16:9 aspect ratio--it was thought it wouldn't matter since most households in America hadn't really made the "shift" to HD (then 420p) and even at that resolution over a standard "box" 240 or 320p color TV - Warner Bros. gambled it wouldn't make much difference.
As time passed, HD players / Blu-Ray playback and recorders could "read" all these different playbacks and compressions and that's why the 3rd looks so bad compared to the first two.
You can take each of the next 5 movies the same way with each director and cinematographer selecting the "best" digital camera..ever improving but until you get to 1080p..or above to UHD or 4K to 8K, you basically can't beat 35MM cinema film..just the DVD or players got better at "compressing" the data to show a higher resolution content in both aspect ratios (Full or Wide Screen).
Again your question is difficult to answer. You almost have to go through each film and examine the director, the cinematographer, which camera they chose and which film format (digital / Blu-Ray /compression etc) Warner Bros. chose for each film when each was released for a 10-11 year time span when TV's finally tipped the scale and went from a "box" for UHF/VHF broadcasts using TV rabbit ears to a home entertainment system in your house with Dolby Sound and High Def picture you got by having to pay for Cable TV. used to only get in a cinema or movie theater pre-1960s to 1999. Great question. That's it.