How to add a time picker in datetime form elements
Your code renders a time type input for the second field, which will invoke the standard time widget for browsers that support it (most modern ones do). 

For all browsers that I know of, that's a simple input mask and placeholders, not a dropdown picker like the date field. If you need such a picker, you'll have to find and integrate a JS library to get it. 

You could do it yourself, but there's a contributed module, Datetime picker, which integrates 3 different time picker libraries so you can choose your favourite. If that doesn't give you exactly what you want, the code should at least give you a good starting point to implement your preferred solution.

In case you still need it, you can remove the seconds from the time input by setting #date_increment on the element to 60, which sets the step attribute on the element. That causes Chrome at least to only include placeholders for hours and minutes.