I agree with most of what you wrote.

Bettering yourself every day is something that makes you who and what you are. -> No, it makes you better aka a different person.

You are building upon your foundation, so you are you, every day of your life on this earth, -> I am me right now, but in the future, I will be somebody else stuck in my body.

Being yourself means to be yourself and not to improve yourself to become better in the future. However, if improving yourself means to be yourself then yeah you could say that I am myself doing that because I will never stop doing that.

To come to the conclusion that improving myself now belongs to myself I had to go through ruthless self-improvement.

This discussion is deep.