Thanks, I think I understand that, though I would put it slightly differently, as follows...

I normally say that probability is not a fact about an event, but a fact about a model of an event, or about our knowledge of an event, because there needs to be an implied population, which depends on a model. When speaking of "situations like this" you are modelling the situation as belonging to a particular class of situations whereas in reality (unlike in models) every situation is unique. For example, I may decide the probability of rain tomorrow is 50% because that is the historic probability for rain where I live in late July. But if I know the current value of the North Atlantic temperature anomaly, I might say that reduces it to 40% - the same event, but additional knowledge about the event and hence a different choice of model with a smaller population (of rainfall data at that place & season with that anomaly) and hence a greater range of uncertainty. Further information could lead to further adjustments until I have a population of 0 previous events "like this" to extrapolate from!

Now I think what you are saying is that subject to the hypothesis that our knowledge of quantum physics is correct, and in the thought experiment where we are calculating from all the available knowledge about the initial conditions, that is the unique case where there is nothing more to know and no other possible correct model - so in that case the probability is a fact about the event as well. The many worlds provide the population, and the probability is that of the event being present in one of those worlds taken at random.

Incidentally, I'm not sure where my picture of probability fits in the subjective/objective classification. Probabilities of models are objective facts about those models, probabilities of events that involve "bets" about missing facts are subjective, while what I describe is dependent on the subject's knowledge of circumstantial data but free of bets, so I'll call it semi-subjective until somebody tells me otherwise!