@Kade_BSG
The full explanation for Wotaku is very long but what you said isn't wrong to a certain extent. The term "Otaku" came from the word お宅 stayed at home, so your perspective is interesting and is kinda somewhat true.
Wotaku originally is a term made by Otakus to distinguish themselves from other Otaku among otakus (especially since there are many types of Otaku like Gun Otaku, Game Otaku, Idol Otaku), so people added W to otaku. That's pretty much about it. I'm sure if you search for it, there's a better explanation out there. Wotaku/otaku doesn't indicate if that person is a working otaku or not. It's just the stigma of Otaku was around longer and the stereotypes are shown in anime a lot, whereas Wotaku is pretty specific that even non-otaku might not even know the terms yet.
People often use Otaku as an insult (Like nerd or geek) whereas Wotaku often used among otaku to politely addressing each other while differentiating the normies. Hence, I wrote it as "a more polite way of saying" etc. Sorry if i have caused a confusion there. I didn't want to TL note to be TL;DR, rather just straight to the point.
Fun fact, even my professor is a Wotaku as well so yeah, it has nothing to do with neet or hikikomori. It's just a stereotype and most NEETs or Hikikomori are Otaku.
To prevent further confusion, i will change it to an alternative yet specific way of saying.