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

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.

The best practice would be to get another disk which is the same size or larger then the one you are trying to recover from. Then do a bit copy if the disk. Uf you can use Linux, (gnu) ddrescue is an ideal tool for this as it will show you progress and give an indication if the disk is failing and try to recover as much as possible.

(If the disk is failing, when ddrescue has as much of it as possible, the udeal is to make a copy if the copy, as the act of recovering data likely further damages the disk. If there is no hardware problem you can skip this, as you can redo yhis if need be)

The next part is wherrle expertise come into it, and the best way to proceed depends on the nature if the failure. I would run it through Testdisk which can attempt to find and recreate partitions, and is often a fast and reliable way if making the disk work.

If that fails software like recuva or photorec can search for files and do partial recovery by identifying signatures. How well this works depends on the data you are trying to recover and the amount of fragmentation. Practically speaking its good for photographs and not much else.

Data recivery experts gave more tools and dkills and its worthwhile consulting them if the data is particularly valuable and not backed up.