External disks used as Time Machine backup failing?

I?o error sounds really generic, but is actually VERY specific. it says a block was unreadable, and after 1,000 retires using error-correction, it was STILL unreadable. The contexts of that block are unknowable, and processes that depend on that data can not be completed correctly.

The only way to clear the error on that block is to provide new data for that block. The quick and easy way to do so fr the entire drive is to erase the drive, just as you have done.

If Disk Utility "First Aid" were correctly named, it would be called Disk DIRECTORY First Aid. it does not read any blocks outside the directory area, and only checks for directory data structures consistency.

Failing Disk Utility First Aid tells you the drive has inconsistencies in its properly-recorded data structures. Those were likely introduced with wonky occurrences over the period you have been using the drive. It says NOTHING about underlying ability of the drive to "do what it was told" and hold specific data patterns.

That test does not measure whether the drive is near death; nor does it indicate the drive is fine.

What was Supposed to give that assurance was SMART status. Unfortunately, Overall SMART status has been a disappointment. By the time that warning sounds, the drive is essentially dead.