Well, post-scarcity really just means that ordinary citizens have free access to replicators (matter-energy converters).
So the closest example (and the only one I can think of where you see civilian Earth, outside of SF Academy / SF HQ or a time travel episode), is probably the double episode in DS9 where the changelings reach earth and there's a false flag event by a corrupt Admiral that causes a momentary power outage and a planetwide lockdown for a few days. I believe it's meant as a 9/11 allegory -- the homeland is attacked and suddenly everyone WANTS a police state, or at least is willing to go along with it, and only the courageous honorable military officers are there to stop the corrupt ones, all the civilians are frightened into compliance.
But post-scarcity? That just means when the security officers aren't around, people can wander into Joseph Sisko's restaurant and eat as much as they want for free, and Joseph Sisko can run his restaurant with as much food supply/ingredients and kitchen equipment as he wants for free, and every gets as much clothing as they want for free, etc. When Earth isn't on lockdown, that's the implication, everyone has as much material goods as they want for free, that's post-scarcity and the implication is they have it.
Post-scarcity doesn't mean infinite resources, or that you can have whatever you want, not everyone gets free land/space on which to build their home, for example. If that's your definition of post-scarcity then I guess at least the Q Continuum has it! :)