I think this is a confusion of definitions.

yes, largely.

Logic describes how our universe works.

No, if you buy a book on logic, it doens't describe the universe.To get a description of our universe in mathematical/logical terms, you have to add in empirical information. There is a convenient shorthand for that: physics. Physics described how our universe works.

So the Great Reductionist Project is .. showing on the way that no part of the universe is not describable within logic.

Huh? How can it show that? Whether there is part of our universe that is not describable by logic is an empirical claim. Science could encouner somethig irreducible are any point.