The solution described in the documentation isn’t suitable for cases where the source drive is dying. rsync will attempt to read multiple files in parallel, further damaging the drive. Furthermore, file-by-file copying is always slower than cloning. Therefore, the best solution for a dying drive is cloning.
However, it’s important to make sure that the drive is actually failing, and not the peripherals or cables, as was the case here - the problem was with the power supply cables, not the drive.
In my experience, it’s always been the power supply, and different manufacturers and different faults can cause this. I’ve only had Toshiba drives die on their own within a year, but that’s a different story.