Even though the _coerce_ and _coerce_c methods are only implemented in the soon to be deprecated sage.structure.parent_old.Parent it is still used in some places. The current situation prevents to build a ring that inherits from Parent and use it as a base ring for the multivariate polynomial ring.

We replace all usage of _coerce_/_coerce_c by coerce and deprecate the formers.

Depends on #33525
Depends on #33576
Depends on #33558

CC: @mezzarobba

Component: algebra

Author: Vincent Delecroix, Travis Scrimshaw

Branch/Commit: 4ed53f8

Reviewer: Frédéric Chapoton, Travis Scrimshaw, Vincent Delecroix

Issue created by migration from https://trac.sagemath.org/ticket/33497