If existential nihilism claims nothing has meaning does it also take moral values in to account?
'Nihilist' was generally applied as an insult, especially around morality - it was first used to insult the rationalism of Kant (who I think no one could call a nihilist now!). It got used somewhat like an atheist equivalent of a Christian calling someone a 'godless heathen'. In Russia it began to be taken up by some of the Russian anarchists of Marx's generation, really because people tried to tar them with that word and they took that 'shocking insult' and said, yes, that is our view. They expanded their rejection of all current political authorities to reject all then existing philosophical authorities on morality.
With Kierkegaard, Nietzsche and Heidegger, nihilism began to take on it's modern meaning, not simply rejecting authority of current structures of thought especially on morality, but rejecting objective value to the sway of implied compulsion of any structure of thought (still the word nihilism alone usually means moral nihilism, and conditionals are added like existential nihilism, for rejecting the universality/objectivity of rationality and intelligibility). These three philosophers did not advocate for nihilism, and it's wrong to call them nihilists.
Kierkegaard saw his interpretation of nihilism, 'leveling', as a challenge rather than a really tenable position. Almost Neitzsche's entire output can be viewed as grappling with nihilism which he saw as inevitable following the losing of sway of Christianity (which had been held more by force, than philosophy) A good article on: Whence Comes Nihilism, the Uncanniest Of All Guests.
Nihilism in earnest in the modern era (Buddhism or at least some schools of, are examples of ancient nihilist thought) begins with postmodernism, what Baudrillard called a 'nihilistic era'. Foucault rejected rationality as fundamental, saying all truth claims are also power claims, so any attempt to have universal morality is a power-grab, and deeply suspect. Like other postmodernists he switched to examining and picking apart texts and claims, rather than building new structures of thought for others to occupy. Kuhn looked at science as fundamentally sociological, and it's 'truths' as embedded in and limited to specific eras and perspectives, which he called paradigms. Still, these postmodernists are called nihilists by others rather than themselves (Foucault didn't even accept being called a postmodernist, another term which is vague & most often used by critics of it).
Antinatalists and advocates for voluntary human extinction or the extinction of all life, are more recent examples of schools which are typically called nihilist, because they reject what others see as a universal value, in this case of life. But similarly, don't identify as nihilist.
Here is a take on nihilism you may find interesting:
Heidegger, Contributions to Philosophy 72. Nihilism, page 109
Thinking in terms of “goals” (the long misunderstood τέλος [“end”] in the Greek sense) presupposes the ἰδέα and “idealism”. Therefore, this “idealistic” and moral interpretation of nihilism remains provisional, despite its essentiality. In aiming at the other beginning, nihilism must be grasped more fundamentally as an essential consequence of the abandonment by being.
That is to say, there really are no goals, but to pretend there are (in 'abandonment') is the real nihilism, (described here).
... no one surmises that precisely this consideration — or, rather, its underlying attitude and comportment towards beings — is the genuine nihilism: the unwillingness to acknowledge the lack of goals.
... the deliberate turning of a blind eye to human goal-lessness, the "ready to wear" avoidance of any goal-setting decision ...
Note the "moral interpretation" is dismantled in the first paragraph.
The new nihilism is a type of dereliction and apathy for which Nietzsche and Heidegger are not advocates but vigorous opponents.