I read that energy is one of the parameters (physical properties) that contributes to the curvature of spacetime, then there is the math proof using General Relativity. I was wondering because common sense tell me energy isn't spacetime but it caused spacetime to curve so which of these two is the cause and which is the effect can't be both at the same time right?
At the local level (that of the equations), there is no cause or effect, only a mathematical identity.
At the level of a spacetime, consider for example gravitational waves: away from their sources, the empty spacetime is in itself responsible for their propagation via the energy they transport which appears as an effective local stress-energy contribution. Asking what is the cause and what is the effect in this context is the same as asking, when considering waves on the ocean, if the shape of the waves are a cause or an effect: the answer is both, because their shape at a given time determines their further evolution, that is their further shape, and so on, that's how they propagate.
Now in the case of the GR equations, there is no evolution because spacetime includes time, so a global solution being a whole spacetime can be considered as static in a 4-dimensional sense and the analogy breaks there (gravitational waves are treated as pertubations, which allows to reintroduce time).
But the point remains that in all systems described by differential equations, causes and effects keep swaping their roles.
It depends on what kind of energy, and which theory of spacetime, you're asking about. For example, electromagnetism and gravitation are not yet united into a single theory of spacetime, so electromagnetic energy would need to be considered a cause of spacetime curvature until a unified theory is developed and widely accepted by the physics community. When/if a unified theory is developed, the electromagnetic field will presumably be considered to be an aspect or consequence of spacetime curvature, so what causes EM energy vs what causes curvature will become an inappropriate question to ask.
Energy is equivalent to mass(e=mc^2) which along with momentum and pressure produces a field on spacetime given by the einstains field equation. To ask what is the cause of this field is like asking what is the cause of EM field which is given by Maxwell equations. According to both theories corresponding fundamental quantities are mass and charge, either which, when introduced in spacetime, cause a disturbance, in the prior fields, which spreads in all directions at c.