That’s a great question that’s been pondered by philosophers for a while: https://en.wikipedia.org/wiki/Ship_of_Theseus

Here’s a fun video talking about the same thing: https://www.youtube.com/watch?v=nQHBAdShgYI

To the contrary, "you" are constantly changing as your existing neurons reconfigure themselves. Replacing them would have at least the same effect.

What makes you sure? Central nervous system neurons are incapable of regeneration[0], so is anybody's guess what would happen if they did get replaced. And, long term, "significant" has to be "all".

[0] https://en.wikipedia.org/wiki/Neuroregeneration

People can have rather serious strokes that kill large number of neurons without losing their sense of self. Sometimes we remove half the brain

https://en.wikipedia.org/wiki/Hemispherectomy

That gives me confidence that replacing neurons at a rate that counters natural aging does not significantly alter me.