I did a bit more work on it this morning. I took the PCB off and was able to turn the spindle by hand, it did seem a little tight at first. I turned it by hand for a few minutes and put it back, no luck, the drive didn't spin up. I did it a couple more times, same result. There is a connector in one of the photos that I put a red rectangle around, that connector looks to run from the PCB down to the motor that turns the spindle. I checked voltage at that connector, the three pins on the left (brown, yellow, red) all had 13.2v, the other three didn't show anything, maybe grounds? This suggests to me there is power going to the motor, so I think it's not a good sign the drive won't spin.
The other definitely-not-good thing I noticed is the two small components in the corner by the blue connecter seem to have catastrophically failed, as seen in the photos. I wouldn't think that would stop the motor from spinning though as long as it's getting power, which it seems to be.
I'm not quite sure where to go with it from here. I imagine I could get a PCB from another drive, but if the drive itself won't spin up, that's an issue. I haven't yet looked into whether there is a utility out there that could low-level format a replacement drive so the HyperDrive would work with it. A really quick google search shows there are a couple devices that emulate MFM drives and use and SD card, though I have not looked into those, and maybe there would be formatting issues involved there as well.