I have two Apple devices that I actively use. An iPhone 6s and a 10.5" iPad Pro. I use the iPad for flying and video/image editing, and a few other, simple things, and my phone is my phone, and it's too small for flying IMO.
So, when iOS 13 was released, I updated my phone, but I did not update my iPad - yet - and thanks to this thread, I probably will not until this issue gets worked out.
I have the Apple SD card reader, and I have used it countless times on both my iPhone and iPad, and it has worked perfectly every time. Unlock the phone, plug it in, up pops the Photos app, and go to work. Not anymore on my iPhone... Now, as far as I can see - and, as
@Radpuppy mentioned above - if you go into your 'Files' app, you can browse the contents of your SD card and save what you want to your Photos, but I found it buggy. Of the 150 or so pics on my card, only half loaded a thumbnail, while the others just had an icon of an image file but no thumbnail. It was so easy before...
IMO, iOS 13 was not an upgrade. It was a very poor update with a bunch of new emojis that I will never have a reason to use...?