I was looking at "get the basics straight", but it doesn't seem to have an entry in any dictionary as an idiom, why is that, and what do you call an idiom that's not an idiom, or a phrase that didn't become an idiom yet, yet has all the appearances of an idiom?
A neologism describes a relatively recent or isolated term, word, or phrase that may be in the process of entering common use, but that has not yet been fully accepted into mainstream language. Neologisms are often driven by changes in culture and technology, and may be directly attributable to a specific person, publication, period, or event.
There are many kinds of neologisms, including the often-amusing portmanteau -- the combination of two words (or short expressions) into one. One example is the now-commonplace "brunch", a mix of "breakfast" and "lunch" as a name a late-morning meal that is neither one nor the other.
I don't know if "get the basics straight" would be considered a portmanteau, since it's not a simple word, but it's the same general idea.
In "get the basics straight", I think you are combining two separate expressions: "get [s/th] straight" and "the basics".
However, Merriam Webster does list "get [something] straight" explicitly as an idiom.
I think whether something is an idiom, or just a group of words with a definition, is really a matter of opinion.
There are also combinations of words (and maybe existing idioms) that are just creative products that individual speakers come up with to express what they want to say. I think "get the basics straight" is one of those.
Maybe you are right in your suggestion that if they are interesting and useful enough they could catch on and evolve into idioms. At some point I guess they could evolve past that point and just become regular multi-word parts of speech (like "flat tire", "pine cone", or "sit down").
It looks to me like "the basics" is no-longer an idiom, but just a regular use of the word "basic", and "get something straight" is in transition. It's an idiom in Merriam Webster but just a standard verb phrase in MacMillan.
As to your question, "what are idioms that aren't yet idioms called?" I don't think we have a standard word for it. Maybe a "proto-idiom."