More quick due dates / use current time when selecting quick due date

I saw that in 1.6.0 there is this new "quick due date selection" (not sure how this is called officially):

For these buttons I have three suggestions:

When clicking the buttons on the left, the time is set to 23:59 automatically, but personally I would like to have it set to the current time (or maybe next full hour).
I.e. when it is 13:26, maybe set it to 14:00.

Totally nice would also be to have some buttons like "next monday" - as I usually have certain meetings on certain dates... An option to be able to configure those buttons would be really nice!

Yet another nice feature would be to have buttons like +1h, +1d, +1w which would extend the current due date by the given amount.

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Start by locating the quick due date selection UI described in the issue and determine which of the proposed behaviors is in scope. The issue needs a maintainer decision on current-time or next-hour selection, preset dates, configurable buttons, and relative extensions before completion can be defined.