I'm not sure if I'm missing something, but it looks to me like both the types and docs for EuiDatePicker each list props from react-datepicker that are intentionally not supported by EuiDatePicker.

I noticed this with todayButton, but after a quick look at the code I believe monthsShown,showWeekNumbers,fixedHeight,dropdownMode,useShortMonthInDropdown,timeCaption,disabledKeyboardNavigation,isClearable,withPortal,showMonthYearDropdown are also affected.