When you think about it, there's a lot of stuff that'll still be scarce even when we have magic robots that can build everything instantly.
Many sought-after things are scarce. Starship commissions are scarce. They require hard work and are assigned based on merit. Not just anyone gets the opportunity to explore the edge of space; it takes dedication and sacrifice.
The show is certainly influence by the philosophy of Stoicism[0].
By the definition of economic scarcity it will be required to in order to merit the name. However, that illustrates that a post-scarcity society will never exist (or at least is vastly farther off than some people imagine), which is the more critical point.
If anything that anyone wants is limited such that enhancing one person's realized utility is a trade-off with someone else's realized utility, you don't have a post-scarcity situation.
Which is why post-scarcity isn't really something we are ever likely to need to worry about.
What we need to worry about is a scenario with scarcity where large masses of the public are (some in a static way, and some in a transitional way that, with optimal policy, could resolve given time), through arrangement of capital and the relative utility of automation vs. labor (including when it comes to producing additional automated production units) unable to contribute significantly to output, and thus have nothing to sell in the marketplace.
You'll notice that the crew quarters in the show are decorated in a minimalist style. The only objects people keep are the ones that are important to them. Tools, games, gifts can be conjured as needed and recycled when you're done with them.
Scarce resources do exist, however, especially on a starship: crew quarters are probably not all of the same size, for example. Some people might have to walk a little further to the turbolift (elevator). These sorts of resource allocation problems are likely solved by either a lottery method or based on need. For example, if the Captain gets bigger quarters, it's not because she's the captain, it's because she might need the space to host visiting delegates, etc.
Although I suppose there are still some material inequalities based on rank. For example, ensigns get a single rank pip, while a captain gets four.