^But doesn't the Prime Directive only apply to pre-warp cultures?
No, it does not — the Prime Directive is cited several times in the TNG+ era as forbidding interference in warp-capable civilizations (this is why Picard doesn't intervene in the Klingon Civil War once the Duras forces start attacking the newly installed Gowron, for example). Note that "interference" in the context of a warp civilization does not mean "no overt contact, period" as it seems to do in the case of pre-warp — it means things like not taking sides in their wars (internal or external) or political machinations as well as leaving them alone if they order you out.
Of course, confusion on this point is natural in that the writers were hardly consistent in what, exactly, the Prime Directive demands (and many episodes and films just blew off the whole thing).