I understand your point, but please allow me to convey mine.

Can you construct an experiment that would, if successful, prove or disprove logic, without relying on logic as a means to determine the proof or disproof?

If it can’t be done, then it would seem like everything that has ever been proven relies on this assumption of the value of logic as a means to gain knowledge about the universe, which you know, is fine… but it hasn’t been proven or disproven, which imo would make it fall under the same categories you mention, as it would seem like what is a part of reality and what isn’t couldn’t be determined without using a fundamental axiom that is taken for granted.

Just like what you are describing in your third paragraph, which are all judgements of value which assume behaviors, beliefs and world views as a means to achieve a better society or life or rely on other unproveable assumptions of value that are impossible to prove, logic also seems to me like an assumption that is impossible to prove.

Not trying to convince you, though. I just wanted to explain my perspective.