OCTADE
@octade@soc.octade.net
The suggestion at the end of this might be a viable option.
Use application, 'testdisk' to analyze without writing any changes. If it can detect the lost exfat tables then it can be recovered. I have done this with multiple failed media and drives. Be sure to read the documentation carefully before running it.
Exfat writes a backup boot region. Testdisk should be able to check for this.
If that doesn't work there is ddrescue and photorec for finding and recovering individual files.
You might also use 'dd' to raw copy the damaged volume to an image file and write that image file to other external media then try running 'testdisk' and other tools on the copy. You can keep the image file as a backup as you try to recover the data from a copy first, to avoid the risk of further damage to the card.