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A map from $\mathbb{Q}[w2,w1,x,y]$ to $\mathbb{Q}[w1,x,y]$ is always going to be tricky because it's just a partial map. I don't know why the block order gets in the way, but it's not hard to work around it:

sage: S(QQ['w1,x,y'](f2))
w1*x^3 + w1*y + x^2 + y^2