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Apparently the symbolic ring considers that SR(eq_z) is a constant.
Compare:
sage: p = (5*x^2-7*x+4)
sage: p.coefficients()
[[4, 0], [-7, 1], [5, 2]]
and
sage: R.<t> = PolynomialRing(ZZ)
sage: I = R.ideal([t^2-2])
sage: S.<z> = R.quotient_ring(I)
sage: eq_z = (z+1)^2-5; eq_z
2*z - 2
sage: a = SR(eq_z); a
2*z - 2
sage: a.coefficients()
[[2*z - 2, 0]]
So it's the constant 2*z-2 times x^0.
