A search term is 'proper postpositive'. This has been discussed in other answers:
proper -- can this postpositive adjective be substituted for "in and of itself"?
https://english.stackexchange.com/questions/354077/use-of-proper-as-a-postpositive-adjective
From wiktionary:
(usually postpositive) In the strict sense; within the strict definition or core (of a specified place, taxonomic order, idea, etc).
Which matches the Cambridge definition you mentioned:
"belonging to the main, most important, or typical part"
It's the "core" part of something. The object in the strictest sense of the word.
The word "itself" is more general, and can be applied in multiple ways, but the main sense here is "The object, the thing, 'by itself', separately, and not dependent on other things."
"Itself" is closely related to "himself", which could be used in an example:
He finished the repairs (by) himself.
That is, without assistance.
If A and B are clearly different things (already), and we say A itself (without B) , that means A separately from B, and without dependence on B.
Going back to "proper", that's referring to the "core" essence of something. The real city, and not the suburbs.
There is similarity between "proper" and "itself". The word "itself" is used to point out a separation and a difference between two things. X and not Y. But usually in the case where X and Y aren't being confused with each other. "Proper" is used to distinguish between the "core main" part, and the "extraneous extra" parts, and when perhaps those two things were confused with each other.
Best Answer
Conditionals are negative polarity contexts, just as much as negative statements, and questions:
Negative:
Question:
Conditional: