Any research on IQ (general) and coping with abstract concepts? Is there any good research on how general IQ correlates with levels of abstractions people can easily handle?

I understand, that abstractions are different, but here it's probably enough to cover base logical reasoning, set (in math sense) membership and such, maybe some other classification. Also, of course there are situations when language already contains metaphors, which allow people to reason (like "file" can be put into "folder"). My question is more about situations, when there are no suitable ready metaphors ("X" can contain "Y"). (memory can also be a factor?)

The notion of complexity of abstract concept systems is also interesting (if there are several), but my hope is to find an answer for any good notion. Basically, "common sense" logic whatever it is is probably enough reference point.

The idea is simple. Lets say, people with IQ greater than X can understand and recognize part-whole relationship and use that understanding in their work. Then, of course, it is easy to calculate how accessible some system is: IQ has very simple statistical definition (given standard deviation).

I am not a psychologist so I do not quite know even what are the right terms to search. However, my interest is in making software applications accessible to more users and user interfaces oftentimes rely on users handling of abstract concepts. So my interest is pragmatic. Still I think this question is more on psychology side than UX.

I believe IQ matters because if a user can't figure out something in a "moment" (in seconds), system is not usable.
I think the answer here is easier than you imagine. Many of the tasks associated with IQ and general intelligence tests contain tasks that are specifically about abstraction. For example, an SAT reading comprehension question depends on verbal and reading skills, but tasks like in an IQ test (e.g., https://en.wikipedia.org/wiki/Raven%27s_Progressive_Matrices) don't correspond to any existing verbal or other knowledge and are therefore tapping a type of abstract thinking.

If that's not what you meant by abstract, consider researching what kinds of cognitive operations are associated with the types of abstraction you had in mind.

Also, note there are a lot of threads in this group about intelligence, and many of them cover the same useful ground, such as different types of intelligence, the difference between IQ and general intelligence, etc. Wikipedia is also a good source on those definitions.