Puis-je te servir un verre ?

English Translation

Can I make you a drink?

I’m surprised that « make » is a translation for « servir ». Usually making someone a drink has an element of mixing it or preparing it in some way, rather than just bringing it or pouring it. My understanding of servir is more an element of service rather than concocting or preparing. Is there another meaning of servir that I am not grasping?

No hidden meaning, your observation about the too liberal translation is correct.