See: #10963 and follow up for details
This is a follow up to #13394 #15069, and a blocker for #10963.
Depends on #15432
CC: @sagetrac-sage-combinat @vbraun @jdemeyer @simon-king-jena
Component: performance
Author: Nils Bruin
Branch/Commit: u/SimonKing/ticket/15506 @ 6147777
Reviewer: Simon King
Issue created by migration from https://trac.sagemath.org/ticket/15506