It seems the largest issues are related to reusing an SD card and even more critically, using the auto review functionality on the a7R III. Sony says the card should still preserve most of the data, as the corruption seems limited to the image database, although the data being written at the time of the interruption may be unrecoverable.
If the images are no longer displayed, they provide the following steps for recovery: Select MENU → (Setup) → [Recover Image DB] → desired memory card slot → [Enter]. Then, take a picture, back up your data on a PC or other device, and format the memory card on your camera.
For the a7R III, there is no solution offered for the auto review bug. The only option is to disable auto review, as the alternative of random lockups can cause data loss. Sony mentions that a software update will be available in mid-December and should definitely be something that Sony shooters are on the lookout for if traveling or using their camera over the holiday season. Before that update is available, Sony suggests formatting the memory cards in both slots before each shoot. Keep in mind that formatting the card will permanently delete all the files on the card. Additionally, a7R III users will need to turn off the auto review function.
For users of any camera, good memory card “hygiene” is important: some rules of thumb include not deleting images from a card from the computer, formatting the card outside the camera, or using the card in multiple cameras without formats in between.