I am not sure whether the following is to be expected.

Martin

sage: R.<x> = SR[]
sage: S.<z> = R[]
sage: (x*z).quo_rem(S(x))
---------------------------------------------------------------------------
TypeError                                 Traceback (most recent call last)
File ~/sage-develop/src/sage/rings/polynomial/polynomial_element.pyx:11713, 
in 
sage.rings.polynomial.polynomial_element.Polynomial_generic_dense.quo_rem()
  11712 try:
> 11713     q = R(q)
  11714 except TypeError:

File ~/sage-develop/src/sage/structure/parent.pyx:897, in 
sage.structure.parent.Parent.__call__()
    896 if no_extra_args:
--> 897     return mor._call_(x)
    898 else:

File ~/sage-develop/src/sage/categories/map.pyx:788, in 
sage.categories.map.Map._call_()
    787 
--> 788     cpdef Element _call_(self, x):
    789         """

File ~/sage-develop/src/sage/rings/fraction_field.py:1254, in 
FractionFieldEmbeddingSection._call_(self, x, check)
   1250 if check and not den.is_unit():
   1251     # This should probably be a ValueError.
   1252     # However, too much existing code is expecting this to throw a
   1253     # TypeError, so we decided to keep it for the time being.
-> 1254     raise TypeError("fraction must have unit denominator")
   1255 return num * den.inverse_of_unit()

TypeError: fraction must have unit denominator

During handling of the above exception, another exception occurred:

ArithmeticError                           Traceback (most recent call last)
Input In [41], in <cell line: 1>()
----> 1 (x*z).quo_rem(S(x))

File ~/sage-develop/src/sage/structure/element.pyx:4498, in 
sage.structure.element.coerce_binop.new_method()
   4496 def new_method(self, other, *args, **kwargs):
   4497     if have_same_parent(self, other):
-> 4498         return method(self, other, *args, **kwargs)
   4499     else:
   4500         a, b = coercion_model.canonical_coercion(self, other)

File ~/sage-develop/src/sage/rings/polynomial/polynomial_element.pyx:11715, 
in 
sage.rings.polynomial.polynomial_element.Polynomial_generic_dense.quo_rem()
  11713     q = R(q)
  11714 except TypeError:
> 11715     raise ArithmeticError("division non exact (consider coercing to 
polynomials over the fraction field)")
  11716 for j from n+k-2 >= j >= k:
  11717     x[j] -= q * y[j-k]

ArithmeticError: division non exact (consider coercing to polynomials over 
the fraction field)
sage: 

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