Have you considered perhaps you're underestimating what happens when one entity can be highly intelligent about everything?
We see a lot of highly effective people that are experts in two domains. I'm not sure we have examples to look to, but I think an intelligence that can run in parallel and is an expert in N domains is going to be a Big Deal.
I do like your thoughts on it not knowing the future, or having omnipresence. I hope those remain powerful barriers for AI.
https://en.wikipedia.org/wiki/Supermind_(novel)
which like a lot of science fiction confuses high intelligence with E.S.P. You could increase the number of coefficients in Chat-GPT 1000 times and it won't be able to tell you who won a sports game that happened last weekend if it was trained a month ago unless somebody told it. (Bing Chat succeeds at this because it gets fed information on demand from Bing.) To do otherwise would be "E.S.P."
I think there are various practical limits on intelligence and I'm not sure if a higher intelligence could really do much more than we can. For one thing there are various results such as
https://en.wikipedia.org/wiki/G%C3%B6del%27s_incompleteness_...
https://en.wikipedia.org/wiki/Halting_problem
and just because your model of computation is based on neurons instead of opcodes and registers does not make those limitations go away.
If people are not making progress on a "theory of everything" or other tough problems in fundamental physics such as "What is dark matter?" it is not because they aren't smart enough to work out a theory. There are many theories of quantum gravity today and many ideas about what dark matter could be. To prove one of them would take a difficult experiment that involves manipulating large amounts of matter and a higher intelligence still has to do that experiment.