The death of God idea by Nietzsche is not about a real being actually dying. It is about the concept losing influence on society and what that means for things like ethics.

Socrates and Buddha were 2,500 years ago and I don’t think I’d describe them as being secularists. Secularism is something that came out of the Enlightenment, in the West at least. It is absolutely a recent thing for the purposes of the discussion.

To describe Buddha as a secularist would be projecting our modern values onto a man 2500 years ago.

Reincarnation, the soul, karma, etc aren't exactly compatible with materialistic secularism.