Just upgraded to 2.4.3. Also have latest DataObject_Manager module (r521). When I click on a declared DatePickerField in the CMS, nothing happens. No popup. Also cannot click into field to edit manually. Is there anything I can provide to help you debug this? Seems like a script is missing or something like that.
Correction-- this is ONLY broken in SAFARI. So, I'd say it should still be fixed, but in the meantime I'll simply use a different browser. I just usually use Safari for SilverStripe because it's the fastest.