What I’m referring to is this. A view of all the notes of a certain date at a glance. Without jumping to the search. The calendar in die side panel just shows calendar entries, not notes.
In general I like your approach of having everything in project notebooks. Maybe I will adopt some of it. Except that I really see it beeing neccessary to have a date on every note, to know when I wrote it down.
And there we are coming back to your OP of moving checklist-notes to the next date/to today/to tomorrow. As @trebso mentioned this leads to an overwhelming and more annoying endless list of tasks like in a classical task manager. Because you add items that can not be ticked off for some time as the project has to evolve first and they become always visibile despite not beeing important atm. The „On the Agenda“ seems more practical. You have the date of the note itself and therefore know when you created it - for the record - and at the same time it is an „unfinished“ „On the Agenda“ task sitting in a separate list. This also may lead to an endless list, but so you don’t keep setting new dates for notes.
Because I want to be able to review when I added something, I can not have notes without dates and coming back to my first paragraph it is helpful to have the calender visible mit markings for dates with notes.
This again just shows how I see this app and how I work with it. Mainly to know what I did at a certain day. As it is sometimes hard to keep track. I sometimes get the feeling I got nothing done and I’m wondering what I did all day. This app helps me to see all the inbetween and little things that come up during a day. Or maybe I just have a bad memory. 
Thanks for reading!
Markus