I regret to say that your external drive had reached its end of life.
All the reserved space for replacing the bad sectors have been taken up. No vacancy now. So the drive controller puts a blanket ban - no more writing. Write protected. Come to think of it even formatting or zero filling involves writing to the disk.
If the HP USB Disk Storage Format Tool and the HDD LLF Tool get the same write-protected error, I would consider your disk as beyond redemption. The write protected error comes up with pendrives too at the end of their life.
You may still try the HDD manufacturer's Hard disk Drive Diagnostic/Repair Utility as a last resort.
( I would be happy if I am proved to be wrong.