How does the rate of reaction affect activation energy?
Activation energy is a fixed amount for a reaction - a constant which is derived from the bonds in the reactants which need to be broken so that the products can be formed.
It is of thermodynamic importance as to what the numerical value of the activation energy is.
The rate of reaction, however, is of kinetic importance. That is a question of how quickly the bonds break, not how easily the reaction proceeds.
For the same reaction, it is the same binds that need to be broken, so the same amount of energy that will be needed to do it. The only thing that can affect the activation energy is using a catalyst - that introduces a new reaction pathway, so it is not really the same reaction any more.
Hayek explains some of this in a video.