For this situation you probably are best to have the HDD unit installed as an internal drive, as you have done. Further, trying Easeus was a good idea. But more is needed.
If Windows Disk Management can see the unit and tell you its space is Unallocated, that means that Windows itself cannot understand the data at the beginning of the HDD - probably in the Partition Table. That could mean two possibilities:
1. The data there was written by the WD Mybook unit in a non-Windows-standard form, so Windows is perplexed. This may mean you need to contact WD's Tech Support people for advice on how to recover the unit's data. It is very likely that the data are all there, but accessing it is the problem.
2. If the Mybook system did not use a non-standard way of doing things, it MIGHT simply be that there is only a small amount of info in the Partition Table that is corrupted. In this case there are a couple of possible solutions. One is to use Partition Recovery software that just tries to sort out the info in the Partition Table and Directory so that the unit becomes readable again by standard tools like Windows. The other approach is more general and uses Data Recovery software to find all the files on the unit and copy them to another storage device. Easeus is one of these. Others are Recuva and GetDataBack, and there are more. Many of these you must buy (although lots of them have a way to "free trial" them so you can determine whether they really can do your job properly), and some are freeware.
Almost all of these recovery utilities have one important characteristic. The do NOT write to the troubled disk, in order to ensure that they do not cause even more corruption to fix. Instead they write the data they recover to a separate storage unit. When they are done, you can they copy all that stuff back to where you really want it to be permanently stored. So, this means that, in order to recover your stuff, you will need (at least temporarily) a spare HDD at least as large as the troubled one, connected into the same computer.