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If the monomial ordering is suitable (see the documentation of PolynomialRing for the options), then you can use:

sage: P.reduce(R.ideal(x*y - w))
5*x*w + 6*y*w + 7*w^2 + x + 2*y + 3*z + 4*w

This assumes x*y > w in the monomial ordering.

If the monomial ordering is suitable (see the documentation of PolynomialRing for the options), then you can use:

sage: P.reduce(R.ideal(x*y P.reduce([x*y - w))
w])
5*x*w + 6*y*w + 7*w^2 + x + 2*y + 3*z + 4*w

This assumes x*y > w in the monomial ordering.