Aargh! Sometimes I really hate me. How could I not see that.
Thank you so so much.
Yes, querying by field values of the date-time-picker is described here.
However, I’m struggling to do the same as I described here. Any ideas are appreciated.
You have to edit the theme templates and add the_field('$FIELD_SLUG');
at the place you want to show it in the frontend.
See more here.