Under one interpretation I wake up in the other room. In the other I do not - it is some other doppelgänger which shares my memories but whose experiences I do not get to have.

I don't understand how to distinguish "the clone is you" from "the clone is a copy of you". Those seem like identical statements, in that the worlds where yon continue living and the world where the clone replaces you are identical, atom for atom. Do you disagree? Or do you think there can be a distinction between identical worlds? If so, what is it?

He isn't me. He is a separate person that just happens to share all of the same memories and motivations that I have.

In the same sense, future-you isn't you either. But you are willing to expend resources for future-you. What is the distinction?