What even is this question? Only about his indifference to death, or all of his philosophical impact?
Socrates was paradigmatic in defining philosophy, philosophy was exactly defined by what Socrates did, though once defined it could be applied retrospectively. And Plato's Academy, and so academia, is the fusion of the Socratic method, and the Pythagorean math cult.
I would put Socrates in a key position in regard to defining philosophy, because his story, and especially his 'martyrdom for wisdom', was the lense, that previous roles were focused into one by: into what was distinctly 'philosopher'. That is, not sage or mystic, but someone actively going out and questioning people, helping them to think through answers, in Socratic dialogue. His choice to accept the hemlock instead of exile (like Aristotle did) was about staying true to his role even over life. Like Digenes, he put his money where his mouth was.
I'd argue there is a crucial difference between pre- & post-socratics, due to this. And that what happened in Greece was subtly but importantly different than in Egypt, India or China, for complex reasons (the Needham question implies, mainly geography).
Aristotle was tutor to Alexander the Great, who's pursuit of his own legitimacy put huge resources behind promoting Greek scholarship, and copying texts.
Wisdom is out of fashion in philosophy, but I argue here it's never been more needed in the world: Wisdom and John Vervaeke's awakening from the meaning crises?
It would be sensible to recognise I willingness to die fir things beyond pur own life and our own genes as a cornerstone of civilisation. No army or war can happen without it. And no unusually good method of living defended without those. This is an ancient human programme, to heroise people that choose to die for things beyond themselves. It's power can be corrupted, in the search for 'kleos', eternal renown. I like this discussion of pursuit of it's hold on us: Lies of Heroism - Redefining the Antiwar Film.
To live with integrity is to live reconciled with your whole life, not be subject only to now. To withstand the intimation of Eternal Recurrance. And that is the true source of people who's lives outlive them.