Watch Return of the Jedi again. All the characters make it very clear that the station is still under construction. Vader berates Moff Jerjerrod for not working more quickly, and Palpatine leaks info to the rebels to convince them that the laser doesn't yet work.

You can also just read the wiki page you tagged to your own post there.

Yep, as was stated above, The Death Star was still under construction, it was not working as a base yet, in other words, the rebels murdered a bunch of engineers, plumbers, cooks, etc.

Yeah pretty much it's still not built properly in The Return of the Jedi which gave the Rebels the advantage to destroy it

^^ The good news is in the OT it's heavily implied that most had the chance to evacuate, those that wanted to. In Canon, however, the Rebels attack the evacuees.

Some time ago I thought the unfinished part was finished but was being camouflaged

During Return of the Jedi, they were building it still

And yeah that's why the outer shell looks unfinished