I suggest to extend the date picker for supporting week and month pickings. Actual behaviour of the date picker is picking a day only. I’m using ACF for an form to input a weekly menu and it would be nice to have a switch in the field configuration to select a date group aka week or month.
WordPress/PHP knows fields to extract the month number and the week number of a date so the internal extraction of this info is not a big problem.
I’ll mark this for the developer to take a look at.
Until then you might do something like “Week starting on date” and do the calculations needed yourself. Not exactly sure what you exact needs here are or the details of doing it though.