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There are a number of tests ... is SR in the Sage library, as found by git grep 'is SR' src/sage/
These tests ignore symbolic subrings, as constructed by SR.subring(...).
All or most of these uses should be changed to isinstance(..., sage.rings.abc.SymbolicRing) or isinstance(..., sage.symbolic.ring.SymbolicRing) (if the module already imports other things from sage.symbolic)
In addition to handling the case of subrings, this will help with modularization (#32601).
We leave a few uses of is SR to follow-up tickets #31988, #31999.