Going by your definition of "productivity", I would generalise by simply grouping anything/activities one enjoys doing or not doing anything as being productive. If volunteering, giving tuition without payment consideration, visiting aged parents/relatives in addition to gathering with friends.... etc... etc. makes you happy, it's productive, so be it.
For not working retirees, there's no weekdays or weekends. There's no "weekday voids" as such. I do however, schedule certain activities outside of holidays or weekends to avoid competing with the working crowds whose timetables may not be as flexible. E.g., my gathering with friends are usually scheduled on non-holidays.
Imho, at the end of the day, to each his/her own. If one worries about how to spend time "productively" or "meaningfully", which may be main stream ideas that are often preached and exemplified by "role models", that's not my retirement. Retirement to me is simply choosing what I like to do which pleases me, not others. Visiting aged parents makes me happy, therefore I do it, not because it will win praise from others that I'm filial or avoid being criticised as unfilial.
Quite philosophical huh. But that's the selfish me who have endured a working life to achieve a deserving retirement