The MIP backends should be tested using a common TestSuite. Right now each backend uses its own doctests, which have slightly diverged from each other, so there is nothing (other than the fact that they were the result of copy-paste from each other) that ensures consistency. (#20296 fixes several wrong doctests in GenericBackend, from which I tried to copy-paste, for example.)

Depends on #20326

CC: @dimpase @nathanncohen @videlec @vbraun @nthiery

Component: numerical

Author: Matthias Koeppe

Branch/Commit: 7138fa0

Reviewer: Thierry Monteil, Dima Pasechnik

Issue created by migration from https://trac.sagemath.org/ticket/20323