The date picker only has default values that are date/time related, with no connection to collection values (even if the screen has the right data links).
When editing a collection record that has a date value, I would normally use the date picker component again to allow the user to edit that date (to make sure the date is valid).
These are certainly limitations we need to uncover at some point. These would be great additions to add to our growing feature request list here: Feature Requests | Adalo