The theme of Nietzsche that the entity occurs again and again eternally conduces a belief that it is not supernatural but mere effete to continue with the eternity. Something transcending the reality is super real while something transcending the nature is supernatural. The idea of eternal recurrence without transcending nature is not possible and if it transcends the nature it is supernatural. But Nietzsche does believe in transcending nature otherwise how the superhuman would exist but it is not supernatural that there is no reincarnation in the process of something occurring again and again over the time.
Out of the box a thing cannot recur till it goes beyond the limits of existence which are known to us prior the experience of transcendence. Though transcendence is not possible in the universe which has a finite beginning thus eternal recurrence is in odds with the big bang. The idea of creation starting with a bang denies a thing to recur beyond the point of creation but there might be the parallel universe existing prior to ours or our universe is a simulation of the one we are not a part of. The God exists prior to big bang that there are multiple universes in which the creation commenced ad infinitum. The Supernatural is the doctrine where the creation never was or never would be but existed in a time-space infinitely earlier than our simulation from where flows pure nature.
Nietzsche’s superhuman though recurs but never had a time-space which defines itself as pure nature in existence. If God was a concept that we killed then how could things recur without divine intervention and how eternity unfolds without divine providence. So God never was dead and it is the existence of God among the mythology that is supernatural and as professed by Nietzsche God had the chance of throwing dice but was overcome by the evolution of man, God is dead and the things that recur are not supernatural but mere confirmation of human condition which Nietzsche thought to repeat ad infinitum.