Move Extension options from src/module_list.py to "distutils:" directives in the individual files (part 4: sage.rings) #29786
Description
Follow-up from #29706 (which is NOT a dependency of this ticket):
Taking care of sage.rings.*, except for those few that would need the additional cython_aliases from #29706.
CC: @kliem
Component: refactoring
Author: Matthias Koeppe
Branch/Commit: 1baaa68
Reviewer: Jonathan Kliem
Issue created by migration from https://trac.sagemath.org/ticket/29786