We have formal definitions, it’s anything that can have a grammar, these definitions are incredibly broad, big endian two’s compliment integer encoding has a grammar consisting of two tokens, 0 and 1. All you need is something that can form a sentence and something that can parse it and the thing going on between them is language. Languages vary in complexity but the floor for that is way lower than you are thinking. Simple languages consisting of one or two tokens are still languages.
There are multiple definitions of language, not one. As another commenter pointed out, if you make the definition broad enough it loses usefulness.
> it’s anything that can have a grammar,
"Can" have a grammar is not restricting. "Does" is the correct verb, and that hasn't been proved.
> All you need is something that can form a sentence and something that can parse it and the thing going on between them is language.
OK, you've actually drawn out an important point. CAN the fungi form a sentence?
I can encode the 2nd sentence in "War and Peace" into polypeptides, but the polypeptides are still just an encoding of the language I picked (English? Russian?), and it doesn't make exchange of polypeptides by any other organism (even grad students!) a linguistic exercise.
> Morse code is language, two’s complement is language
Wrong on both points. They're encoding methods. The alphabet is not language, either.
> to think otherwise is incredibly small minded.
Ad hominem.