The screenshot below is from an OOUI datetime picker. As you can see, it provides a way to select the date (calendar), but doesn't really provider a way to select time (has to be manually entered).
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The title of this task is inaccurate, there's nothing wrong with manual entry.
Also I doubt there's really much need for something other than a text field for entering a time, as times are pretty straightforward numbers (unlike dates where day of the week or week in the month make a significant contribution to the way people think about them).