You're equivocating between your stereotype of nihilism and what "real nihilists" "should" do to be considered a nihilist. Nihilism != depression, even if there is overlap, and it's useful to let the words have different meanings.
There are a decent number of people who are nihilists without meeting your assumptions above (though they're probably less salient, as if someone seems functional & not-miserable, people don't usually bother to ask whether they're a nihilist).
Nietzche defines nihilism (partially) as those who oppose the affirmation of life which is kind of related to what you say here... except the affirmation of life requires a "yes" to life such that "all of eternity [is] embraced, redeemed, justified and affirmed,"[0] which I think plenty of (functional, happy-ish) people do not experience.
[0] https://en.wikipedia.org/wiki/Nietzschean_affirmation
[Footnote: Nietzsche is writing against the nihilism he saw in his own time, not in favor.]