Andrew G. answered 12/16/21
College Philosophy/Social Science, and High School English Tutor
So it's worth noting two things: postmodernity is more of an affect and a rejection of the idea of modernist philosophy, wherein the latter believes in prescribing some narrative about progress or some kind of specific conception of what can constitute "good" politics or a life well-lived. So postmodern philosophy is not necessarily a view that invites a positive prescription, but more of one that rejects that philosophy is in the business of ascribing a view like "such and such is the correct political view to hold".
The second note I want to make is in the respect to postmodernism's approach to truth. Postmodernism is not tied to a view of objectivity other than by virtue of ascribing a grand narrative like a political ideology being justified in some way. One could believe the latter while also believing in a kind of objectivity, just not one that is justified by a bigger analytic philosophy that claims to exhaust what truth is.
With that said, the reason nihilism seems popular is because of the acceptance that meaning can't be derived from certain happenings or experiences by virtue of the experiences themselves. This is in part because of what you've characterized as the existential(ist) nihilism: one that denies that our living fulfilling lives can be cashed out with some instruction book on how to live. So people then popularize and linger on this fact, stating that if this is true, it can't be the case that any value can be derived from anything. I characterize this as a sort of defeatism about value, given that they haven't entertained any other idea of how we could derive objective value from anything.