I am also interested in increasing the accessibility of the datepicker widget by adding a role and aria-label to the div created on the popup calendar. I believe the division is
<div id="ui-datepicker-div" .... Something like this will work
<div id="ui-datepicker-div" role="complementary" aria-label="JQuery Timepicker"
An additional accessibility concern is that if more than one datepicker are added to a page they all have the same id.
If more than one datepicker is added to a page the role can stay the same, however it would be best to change the aria labels to make them unique.
I see this issue (#9298) is five years old. Is there an estimate on the rewrite according to the roadmap?