feat(datepicker): use invalid date instead of null when the date input it not empty

### Feature Description

Set the value to invalid date instead of null, when the input is filled, but invalid. As this would be a breaking change, maybe introduce a setting to optionally enable this.

### Use Case

Currently when you use a datepicker without ngModel or reactive forms the input wont get red for invalid inputs and the value is null. So you cant differenciate between empty input and something invalid. Even aria-invalid is "false".

With this feature you could solve this.

Start by locating the datepicker implementation and its handling of filled but invalid input. Review how empty and invalid values currently differ, including aria-invalid behavior, and identify existing datepicker tests before deciding how an opt-in setting should work. Done means invalid non-empty input is distinguishable from empty input without changing default behavior unexpectedly.

Written by the indexing model from the issue text.