Hello,
the volume which the damaged exfat file system is located on is identified as disk 1 by the disk manager, on the previous screenshot. Again, the volume has no partition table.
One can refer to it as a "partition", out of language habit, but for the sake of correctness, I point out once again that it is not a partition. It's a block device, the totality of which being formatted in exfat.
That is where I fear the main difficulty lies.