Found directory entry beyond end of directory in (file path here) while running first aid on corrupted external HDD drive

You should check the health of the drive by running DriveDx (free trial period available) and posting the complete DriveDx text report here using the "Additional Text" icon which looks like a piece of paper on the forum editing toolbar. You will need to install a special USB driver, however, even with the special USB driver some adapters/docks/enclosures will not allow the necessary communication to access the health information on the external drive.

If the drive is failing, then the more you try to recover files, the more likely the failure will get much worse where even a professional data recovery service will be unable to recover any data. If the drive is failing, then you are making the failure worse since macOS and normal apps & utilities (even data recovery apps) are unable to handle the errors produced by a failing drive.

I highly recommend you stop using this drive immediately until we confirm the health status of the drive. It sure sounds like the drive is failing and the failure seems severe already.

FYI, you should always have frequent and regular backups of all external media (including the cloud) which contains important & unique data. Do not just rely on Google Drive or other such cloud services for your only copy of important data, nor as your only backup copy since cloud services may change their terms at any time or be unavailable when you need them most.

Just as I suspected, that hard drive is in very bad shape. I'm doubtful even a professional data recovery service will be able to recover any data from that hard drive.

The hard drive has just about run out of spare sectors and it still has about 3K sectors pending reallocation. It is those 3K sectors that are causing most of your problems.

Even more alarming are the huge numbers of Uncorrectable Errors which indicates data loss since the drive could not compensate for the errors.

And the Command Timeout is extremely high meaning that no one is likely to get any data from this drive....even a professional data recovery service.

If you still need to retrieve data from this drive, then stop using it immediately...including disconnecting it from power so it isn't running at all. Contact a professional data recovery service such as Drive Savers and provide them with this DriveDx health report so they can provide you with an estimate if they think there is any chance of retrieving data. Drive Savers is recommended by Apple and other OEMs, plus they provide free estimates.

I have successfully performed what I consider advanced amateur data recovery on hundreds of failing hard drives....a few of which were in very bad shape where I thought there was no hope. From my own limited personal amateur experience, I don't think it is possible to recover anything from this drive, but a professional has access to special software and will swap out any damaged components to help facilitate recovery. However, with all those Reallocated Sectors and Sectors Pending Reallocation....this indicates the magnetic surface of the platters are damaged so that is why I don't believe anything further can be done, but it never hurts to confirm with a professional.

Sorry to give you the bad news.