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Newtons are a measure of force, by definition. If you are measuring newtons, you are measuring force.
Spacetime is not mediated by a Newton. It's not mediated by particles which can exert a force as Newtons.
But that's what you would be saying from this dichotomy. If you accept gravity is the curvature of space, and you think its a force, then stating it's a real force that is measured in Newtons.
I think this could be too confusing the whole Newtons thing, because gravity, while it is true the acceleration is a gravitational field strength (g) in Newtons per kg. But the idea of Newtonians field and that described by Einstein are very different.