We’ll do our best to add more options down the line, note that you can already do a search based on date presets (next month, past month) and save those as overviews (premium feature) that auto-update.
As far as I can work out the ‘presets’ which appear in the calendar pop up next to the search bar only relate to the date of the note. They can’t be linked to #due dates.
OP seems to be referring to tasks which would presumably be given #due dates.
I spent ages using the calender pop up and then puzzling why notes with #due dates didn’t show!
Feature request: ability to use a calendar pop up to search due dates - remembering syntax is a pain!