First step, we must somehow understand what "self-improvement" means and how to measure it. Even this idea can be confused, so we need to get a better understanding.

Yes, absolutely agreed. That's the place to start. I'm suggesting that doing this would be valuable, because if done properly it might ultimately lead to a point where our understanding is quantified enough that we can make reliable claims about how long we expect a given amount of self-improvement to take for a given algorithm given certain resources.

This is a bit different from other situations, where you can first measure something

Sure, situations where you can safely first measure something are very different from the situations we're discussing.