I think the post Flood nephilim were 'just' the long-lived giants like the ones Joshua and Caleb eradicated. It was only like 7 or 8 generations from perfect DNA/genetics (Adam) to Noah, and something changed quickly after the Flood that disrupted that even more to where 4 or 5 generations after Noah people are living to be 120 at max instead of 500+ years.

The grandsons of Noah, especially the likes of Nimrod were worshiped as gods. Imagine your grandfather's grandfather's father being alive, but all those in between were dead - and he was still in good health and very powerful/wealthy/knowledgeable. Couple this with clan/dynasty hierarchy and it makes sense why they became legendary. The early Akkad/Assyrian kings were all Nimrod, just like Mizraim=Menes=Misr. Imagine the knowledge someone with like Nimrod would possess over centuries.

Shem, Noah's son was still alive when Abraham was alive. Likewise, that whole region of Canaan was filled with these very old powerful giants (the post-Flood nephilim) who were also very very old. I do not believe they were old or giants due to genetic manipulation but genetic inheritance.