Well, it's still under warranty, but prior to exchanging it, I would like to recover my data and backup it.
My advice is that BEFORE YOU DO ANYTHING ELSE you make a backup if you haven't already done so .
Unfortunately, as I wrote, the HDD regenrator session is intended exactly so as to make backupping possible.
Download WD diagnostics software or check the disk with smartctl from Linux. While I don't have any Western Digital disks myself, I expect that it should be possible to check SMART data from their diag tool (alternatively, there are probably Windows software that can display this as well). If you see SMART reporting bad sectors, the disk must be replaced.
I tried the WD diagnostic tool but it led me to nowhere. Only HDD Regenerator showed recovery power.