But isn't it true to say "that electron state" in my left hand and "that electron state" in my right hand are states of two separate electrons?

It was my understanding that electrons had a ton of possibilities states/superpositions that they only "chose" one when they became entangled, is it wrong to think of all the possible positions as the "electron" and it's current configuration in my hand as the electron state in this branch of the wave function?

Thank you for clarifying. I was looking at my left and right hand thinking "Certainly the electrons in my left hand are not the electrons in my right hand."