Generational wealth generally is used to mean something like you and at least your children can live very comfortably off of investment income for the rest of your lives, I.e. none of you have to work for a living. That’s why sibling’s def of 1.5-5m per child is much closer to the commonly understood meaning.

We can debate “live comfortably” if you want, but no 4.5 people are doing that from the investment proceeds of 1m.

What you are describing is kind of more like social mobility.