AW: Reorganization of the header files (GitHub #9333)

[Dr. Matthias St. Pierre]

> Merge early is pretty much my default position ... and that applies to this context in my view.

Thank you Tim for your quick and  clear consent.

Meanwhile, pull request #9333 and its counterpart #9681 for the 1.1.1 stable
branch have been approved by Richard. Unless I hear any protest until Sunday
afternoon (CEST), I would like to merge in the evening, just in time before the
Australian plumbers start their weekly shift again.

Matthias