If I insert the SD card into my iOS 13 device, I get the option to save videos but then the card becomes blank and the videos are not saved!
So the other way is to use the App connected to the DJI MIMO, painfully slow as it is.
Firstly, it says I do not have enough storage space on my iOS device (not true), so I downloaded a few of them in a batch.  However, it was then impossible to see which ones I had just downloaded.  So the UX is really poor.  It should mark the ones already downloaded.
Secondly it is really unclear what the "App album" is.  Obviously I don't want or need 2 copies of every video stored locally.  I just want one hi-res version in Photos.  It is very unclear how to achieve this.

Hello, there. Sorry for your inconvenience.
For the first issue, may we know which is your SD card? Can the unit recognize your SD card?
For the second question. After you connect your unit to DJI Mimo app, the app prompts you to synchronize the new materials which have not been downloaded to the local album before. After you tap yes or download manually, those materials will go to the local album called "DJI Mimo". The " DJI Mimo" album might be a hidden album. However, you can search and check the materials and their route in the  Recently View
Third, App Album refers to the album in the DJI Mimo.

But I cannot see the point of "App Album".  Most modern smartphones have a means of storing pictures.  On the iPhone, this is called the Photos app.  So by moving videos from the SD card to the app you are clogging up my phone with around 100gb of storage.  The DJI Mimo app is by far the highest user of memory of all my apps.  
Please, what is the reason for you having "App Album"?  
Can I use the Mimo OK and delete your app?

I generally use the DGI software to transfer the images to my iPad. And yes, it is incredibly slow! The other option is to pull the SD card out of the drone, using adapter plug it directly into my computer.   

Could DJI explain how I get the pictures from the SD card (which is displayed in the Files app on iOS) into the app so I can use the AI editor.  Please do not tell me to wirelessly connect to the camera which is 3,000 miles away.  I have the SD card and I have the app.  Thanks.