The APEX date picker is an implementation of JET's ojDateTimePicker.
Have created a standard APEX 21.1 app, with a standard region, and a date-picker using the following attributes:

It works okayish, but for the $%^&! date display button area shown in idiotic format MM-DD-YYYY as pointed at by the cursor below:
06/21/2021 scrunch upped against the Done button area. Really!?
I sincerely hope I'm simply getting something wrong here as that is much easier to accept and fix than an underlying APEX or JET ojDateTimePicker problem...