Can I recover data from a failed hard drive?

Is there any way I can actually recover the data from this hard drive?

The issue is that it isn’t even showing up under "This PC" at all (I’m assuming the culprit is whatever is highlighted in blue on the left side of the image)

Maybe try a different watch cable

What now? Microsoft... you think you can just swoop in and save the day?
It could be a faulty cable, or maybe the HDD pins aren't making a solid connection.
Unscrew it from the drive, clean those tiny contacts, or hit them with some WD-40,
then give it another shot.