Depends on #32776
Depends on #32732
Depends on #32174
Depends on #32889

CC: @kliem

Component: refactoring

Author: Matthias Koeppe

Branch/Commit: 1c028c7

Reviewer: Jonathan Kliem

Issue created by migration from https://trac.sagemath.org/ticket/32846