Does it show up on the system? If you want to diy it I'd give ddrescue a shot and see if it can get most of the data. DDrescue is made for failing drives and can restart, and try to get bad parts of the drive later on.

Typically you can get the external HDD cheaper than a internal drive + a enclosure, so I'd just buy it as one unit.

I'd aim for > 10TB as there aren't any drive managed SMR drives of that size I know of.