So I finally got most of the data off the failing drive, and I backed it up to a second new drive. But when I attempt to fix the filesystem I get this:

[root@localhost-live home]

# e2fsck /dev/sdd
e2fsck 1.45.6 (20-Mar-2020)
ext2fs_open2: Bad magic number in super-block
e2fsck: Superblock invalid, trying backup blocks…
e2fsck: Bad magic number in super-block while trying to open /dev/sdd

The superblock could not be read or does not describe a valid ext2/ext3/ext4
filesystem. If the device is valid and it really contains an ext2/ext3/ext4
filesystem (and not swap or ufs or something else), then the superblock
is corrupt, and you might try running e2fsck with an alternate superblock:
e2fsck -b 8193
or
e2fsck -b 32768

Found a dos partition table in /dev/sdd

**********************************************

Are those the actual superblocks it wants me to try, or just potential examples?

[Update a while later]

OK, when I run it on the partition, instead of the drive, it says the file system is clean.

New problem: When I mount it to /home (where it normally lives on my system), I see nothing in it except lost+found. That’s not encouraging.

[Tuesday-morning update]

For anyone curious, who wants to go through the entrails, I’ve posted the entire session in comments. It remains a mystery to me why none of the drives seem to have data, or how I could have done anything to my source drive that I was trying to rescue.

[Update a few minutes later]

Yes, I clearly screwed the pooch. I accidentally formatted the drive I was trying to rescue.