What's happening to the potential energy of electrons after they left battery?

friends. I am new in the electrical field so I must show my guided point of sides that related to my question before I ask it, for understanding how I think. first, let’s begin with the battery, I learned that after chemical interactions the battery will produce electrons so these electrons will be get accumulated in the same wherein negative terminal of the battery so after that and because they have the same charge so, therefore, they will get energy(electric potential energy ) because that the charged particle they will get electric potential energy if they are in electric field that produced by other charged particle so because the electrons are accumulated then they will get a lot of electric potential energy because they are in an electric field that created by other electrons at the same place so they will try to use this energy to push other electrons and so electrons will use this energy to push other electrons to the circuit but after they do this I heard that electric potential energy will convert to the kinetic energy but how this will work because (the kinetic energy=mass0.5velocity^2) and because these electrons have constant drift velocity. and its thermal velocity is affected by the thermal energy of the substance nor the voltage. so haw the electric potential energy will convert to the kinetic energy and there is the velocity of electrons is not changing cause voltage and the velocity of electrons are called by the thermal velocity that caused by the thermal energy nor the voltage so what happens to this electric potential energy?

I learned that the speed of electrons is very high but are random and we call it thermal velocity because it is caused by thermal energy(temperature of material) and is affected by temperature

also drift velocity is just moving electrons(electrons are moving randomly and the electric field are push them but the electrons still in random motion) toward the positive terminal(depending on the electric field). so the electrons are in random motions and because the electric field makes them go toward the positive terminal and the moving electrons toward positive we call it drift velocity and it is constant

now, what happens to these electrons’ electric potential energy after they leave the battery? it is converted to kinetic energy but how and the speed of electrons isn’t depending on the voltage(thermal velocity..)

does it remain electric potential energy because of the other electrons in the conductor? but after the electrons go through the loads then they lost the energy and there are still electrons in a conductor because there are electrons there and I mentioned that if a charged particle is in the electric field of another charged particle then it has electric potential energy but here they lost the energy and the electric field still here

sorry for my English(I am not English). I searched a lot about this but I didn’t get anything. I hope u understand what I am meaning also there are many things in my head but I can’t translate them to English because there is no translation yet for my native language