I thin the first problem is that 1919 is not wrong. 01/01/19 is just inacurate. I don’t know of any configuration to change this, but you could add an onchange microflow that resets the date to a 20xx date if the entered date is 19xx. But you need to ask yourself where you start with it. For example, what does 50 mean? Is it 2050 or 1950?
There is no configuration setting for this. Not in the regular date selector, not in any of the AppStore date selectors.
The y2k-bug is about dates skipping back to the year 1900 at the start of this century, so that is something different, but I get your analogy. Also, I agree that the choice for 1919 is not what is to be expected. It makes more sense for the date selector to take the closest match.
The AppStore app jQueryUIDateTimePicker does select the closest date, so you might want to consider using that one.