How to recover files from an HDD that cannot boot or be discovered by Windows Explorer after failed Windows update?

In the middle of a Windows 10 update, the computer restarted itself but wasn’t able to boot back into Windows with a boot device not found error. I booted the machine to a Windows Media Creation Tool to attempt to repair the update without success because none of the options available to me (repair, reinstall, rollback) were even permitted. I removed the HDD from the computer and plugged it into a working Windows machine (using a SATA-USB adapter) but could not even discover the drive in Windows Explorer, despite being recognized by Device Manager.

UPDATE

I originally thought, for a number of reasons, that the update was responsible for modifying the drive’s boot sector but one of the contributors was actually correct that the Windows update merely exposed a faulty HDD and consequently put the drive in an unbootable state. This was in part confirmed by the Windows disk management tool which exposed a cyclic redundancy check error.

If this has happened to you, the drive obviously must be replaced and a specialized data-recovery program is likely your only hope at data recovery. I was able to recover everything using Stellar Data Recovery which I now highly recommend.

Answer

CRC errors might more be coming from the USB adapter. I trust SATA/USB adapters way less than I trust hard drives (for reasons of experience).
However, since we did see data corruption on the original system:

I wouldn’t see how an update specifically damages your hard drive. My guess is your hard drive started failing a long time ago, but your system was able to use reserved blocks to work around bad sectors (or something similar). The update was a write-intense workload that uncovered more broken sectors than known before, so that the device now basically went into a completely failed state.

With much luck and patience, a specialized imaging program might first recover a (potentially hole-y) image of your old hard drive, and then you can try to recover data from that. I don’t know any such tools on windows, but on Linux you’d use ddrescue to image your broken hard drive into a file on a different hard drive, and then hope you can extract the interesting files from that. In any case, making an image, which you can copy arbitrarily so that you don’t work on the progressively deterioriating hard drive seems very desirable.