> any JSON or YAML that carries semantics with the syntax is a language

semantics are defined by the converter/compiler/interpreter, and that is the process which is going to consume the said json/yaml. if the json/yaml is going to be consumed by any process then the semantics are inherently defined, so by your definition all jsons/yamls are in their own a "language" (or they are not being consumed at all), which just defeats the purpose of calling it a language at that point.