I regard “laws of thought” like the Law of the Excluded Middle the same way as I do the Law of Non-contradiction (and the “Action Axiom” for that matter) - as redundant and unhelpful responses to failed communication attempts.
As for what constitutes a valid definition of knowledge, that is a fairly deep rabbit hole, so we should expect plenty of disagreement until quite careful definitions are agreed upon.
Schrödinger’s cat is just nonsense, since a belief that the cat is “neither dead nor alive” or that “the universe hasn’t decided” does not pay any rent in terms of anticipated experience. In other words, it is not a belief at all, just a bunch of uninterpreted words that do not do anything to guide my actions - they are meaningless in the deepest sense of the word.
As for Gödel’s theorems, the Gödel sentence doesn’t communicate anything to me at least until it is put in its physical form, which I think has something to do with Turing machines and/or the halting problem - someone might refresh my memory on that.