Is this the result you're looking for?
If so, then, yes, the problem was duplicate vertices - 222 to be exact. Select the whole thing, go to Mesh> Clean up> Merge by distance. When I did this, I still noticed two stray edges bisecting planes near the back (second time I tried I found only one for some reason) - look for them, select them, right click and choose "dissolve edges".
After that, re-select the area you want to duplicate/separate, and it should work the way you intended.
Also, is there some special reason you're separating By Loose Parts, instead of by Selection? By selection is what I used without thinking, and I can guarantee it works (I tried both ways and they both work).