It appears to me that there may be an alternative approach to the description of the difference between formal and informal languages.
This alternative approach could be based on the different types of systems that use the languages as opposed to the characteristics, attributes and properties of any given language.
For example almost all (if not all) machine executable languages are formal languages.
Natural human language spans a range of formality.
As you indicate, formal languages are dependent on syntax rules to support communication.
Informal human language can use the common context shared by the human communicators as a basis to support meaning.
So, what language is in every topic except "formal languages?"
The work appears to focus on written human languages, which must have a degree of formality just to be produced and interpreted.
Another interesting work is "East is a Big Bird: Navigation and Logic on Puluwat Atoll," 1970 by Thomas Gladwin. Puluwat has a verbal, non-written language. Information is passed on by memory and verbal chants. I would say the this is a less formal language. This less formal language is embedded in context. Language terms relate directly to artifacts in the physical environment (East is a big bird).