A few comments:
I gave up on Photostream because it provides no capability to organize images within it. Also, I don’t like the idea of images disappearing beyond my control. Yes, it’s free, but I’m a controlling type. If I need to pay a reasonable rent for Cloud storage, I’ll do it.
Before subscribing to iCloud Photos, I always moved images manually by connecting my iPhone to the computer and using Image Capture to move the photos. I then used the free app EXIF Renamer to rename the files by the capture date and time before importing to my photo program of choice for further processing and organizing. There was never an issue of reformatting in the transfer process.
By the way, I don’t think you have made clear the way the 16:9 shots differ from the square photos. It should be in one of the three following ways:
Are the tops and bottoms of the square photos missing (I.e. the transformation has cropped the square photo)? Have you checked in Apple Photo to see whether you are are viewing an edit of the original photo? If so, go into Edit Mode where should be able to revert to the original. If not, you really do have problem.
Are you seeing extra portions of the images on the sides of the transformed photos? You could fix this by recropping the photos on the target machine. Apple Photos provides the usual aspect ratios as specific options in Edit mode.
It the photo distorted so that the photo fills the screen and objects appear wider than in the original? If so, somewhere a display option to fill the screen or window been selected. So, in this case, the photo is fine, but you need to reverse that option.
Note that the way to get the most data into an image is to shoot in 4:3. Choosing a square aspect while not use data captured on the sides, while shooting in 16:9 will not use data at the top and bottom. If one of the other aspect ratios is required, you can alway crop the original. A good editor will provide an appropriate mask for these common ratios.