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Some people still believe there are no politics in Star Trek
(startrek.website)
As powerful as this scene was, the next one has Rom asking his mom to get naked. Ferengis are the best!
DS9 dabbled into politics in ways the other series never did, to the point of a culture conflict, war, genocide, oppression, occupancy, etc.
DS9 certainly took it to a more intense point, but there's not a single Star Trek series that wasn't constantly swimming in politics, philosophy and ethics dilemmas. Anyone who thinks there isn't real life politics in Star Trek isn't paying attention.
Most of the other series were more philosophical. It wasn't really about the long-lasting impacts of politics, rather more just thought problems that were wiped away at the end of the episode.
I think that's what OP meant when they said "...politics in ways the other series never did".
Also, to put it more simply.
When faced with Q, Picard tried to reason against an unreasonable foe using philosophy. (theory)
When faced with Q, Sisko punched him. (praxis)
Star Trek has been very political since the original series.
And don't forget Miles O'Brien, union man. Or Quark's employees forming a union for that matter
The setting allowed for some deep introspection not distracted by the Planet of the Week™