I would argue that Nietzsche is a philosopher of nihilism, not a nihilist. He saw the loss of the old values (god being dead), and the lack of candidate replacement values. I made the case the abyss for Nietzsche is nihilism: Trying to Understand Quote by Nietzsche in the transition from old to new values (the tightrope over the abyss).
Durkheim the foundational sociologist, gives us a less hyperbolic picture, and the research to back it, of the same thing. In his work on suicide, he coined the modern meaning of the term anomie - loss of personal and social meaning, that leads to social decoherence, and suicides.
Durkheim's work on religion, gave pretty much the first definition that could be applied beyond Abrahamic faiths, to Shinto, Buddhism etc.
A religion is a unified system of beliefs and practices relative to
sacred things, that is to say, things set apart and forbidden-beliefs
and practices which unite into one single moral community called a
Church, all those who adhere to them
-Durkheim, The Elementary Forms of the Religious Life
'Monster theory' interpretation which began with Tolkein, interprets mythological narratives as expressing cultic shifts and other social dynamics. And in this light we can make more sense of Nietzsche's monsters like the dragon 'Thou Shalt': What did Nietzsche mean by monsters and the abyss? And more generally his placing his hopes to overcome nihilism through heroic figures, living out mythologising narratives. We have returned to a 'marketplace' of religions & philosophies, where the threat of murder for heresy and apostasy is not enough to prevent people innovating around ways to support social cohesion.
I like James C Scott's language on this, that there is a 'metis', a craft of living well together, which we accrue given enough time, but that rapid social change challenges the legibility of that craft between generations, if there isn't time to translate utility of the old metis to new generations. Discussed here.
Nihilism should be understood as the recognition meaning and values cannot simply be found, or imposed, by a religious book, or a process of abstract reasoning. It is existential, we have to look to our own lives themselves, and confront the lack of inherent or external meaning. We take for granted social truths and social salience landscapes as real, but the above understanding of anomie, religion, and social cohesion, can help us to understand how not just the personal process of meaning-making, but the social one too can become conscious, and dynamic, rather than rely on mythologising it's objectivity or antiquity.