Why is the next dividend payment missing from my future income in Generator?
Generator treats the date the holding was added as the purchase date of the stock.
So if the holding was added on or after the dividend ex-date then you wouldn't be entitled to the payment since the purchase date was not before the dividend ex-date.
If you purchased the stock on an earlier date and you want to see the correct dividend payments then you need to add the purchase transaction with the correct date.
This article explains how to add a transaction.
There is more detail on holdings with and without transactions here.