First Aid unable to repair corrupted external hard drive

It's important to understand that the Disk Utility does NOT test a drive for physical damage; it only scans & (attempts to) repair the drive's partition schemes / directory structures. ... so what we don't know yet, is if this issue is a more serious drive failure at this point in time. This is where an excellent drive diagnostics tool, DriveDx, will come in handy. If nothing else, it will become a valuable tool in your diagnostics "toolbox".

HWTech, a valued forum member, sums this up with the following quote from one of his posts:

"First off, First Aid will lie to users these days. Always click "Show Report" to manually scroll back through the report looking for any unfixed errors. In fact you should always run First Aid on the hidden Container in order to scan the complete APFS container since all APFS volumes within the container share the same file system. If there are any unfixed errors listed, then you will need to run First Aid while booted to Internet Recovery Mode, otherwise you will need to erase the drive before reinstalling macOS & restoring from backup. For an Intel Mac, I would erase the whole physical drive (do not erase the internal physical drive on an Apple Silicon Mac). Within Disk Utility you may need to click "View" and select "Show All Devices" before the physical drive and hidden Container appears on the left pane of Disk Utility." Credit: HWTech ASC (2023)

First, it is important to know that sometimes First Aid Repair may have to be run multiple times before getting an ok result. If that is not possible then the simple solution is to replace the disk with a new one. Then when you reset Time Machine to store the data to the new disk, it will initially create a new full backup so your data will again be secure. Problem solved.

It seems like that the harddisk is damaged. If you format it, you will lose all of the data on it, but it will not be easy to retrieve the data on it