I haven't seen one example of a precise definition of what constitutes an "observation" that's supposed to collapse the wavefunction in Copenhagen interpretation. Decoherence, OTOH, seems to perfecty describe the observed effects, including the consistency of macro-scale history.

This in my opinion proves that memory sticks with the branch my consciousness is in.

Actually it just proves that memory sticks with the branch it's consistent with. For all we know, our consciousnesses are flitting from branch to branch all the time and we just don't remember because the memories stay put.

We may say we want to predict "what will happen," but I believe by this we mean "what I will see happen."

Yeah, settling these kinds of questions would be much easier if we weren't limited to the data that manages to reach our senses.

In MWI the definition of "I" is not quite straightforward: the constant branching of the wavefunction creates multiple versions of everyone inside, creating indexical uncertainty which we experience as randomness.