The question asked and answered was what are some elements, any elements, that DS9 has in common with [the stereotypical] soap opera and which are not prominent in other Star Trek series. Such elements are readily apparent.
No, they all exist in every other modern series (and some of the movies).
Arcs
TNG:
- Klingon arc, especially pertaining to Worf's honor
- Borg arc
- Q's judgment of humanity
VOY:
- Obviously getting home
- Those dealing with different species/villains such as the Kazon, Hirogen, Borg, etc.
ENT:
- Temporal Cold War
- Xindi and the Expanse
- Augments
Ensemble Cast
For each of the modern series, they all had one. Sure, there was always one character who got the shaft and some who had more story, but as it was in DS9 too.
Characters 'pining' after each other
Aside from what was already said about Odo never actually having Kira, several characters have had these moments in the other series.
TNG:
- Picard and Crusher
- Riker and Troi
VOY:
- Janeway and Chakotay
- Chakotay and Seven
- Kes and Neelix
(There's likely a few I'm missing here, I haven't watched Voyager through in some time)
ENT:
- Trip and T'Pol
The thing about soaps is that they're always open-ended, focus largely only on relationships and sparsely on plot, and appeal largely to a female demographic. Those are what I'd call the defining characteristics.
All the next gen series, despite having arcs, has often still worked with a singular plot and theme that stand alone in an episode. Relationships aren't always the focus, and they do have plots that go beyond that. And the demographic is probably more male than female.
If all of those criteria defined soap operas, they could easily apply to most drama TV shows, which is why they're apparent in all the later series and movies.