I actually think what you are going for is closer to JL Austin’s notion of an illocutionary act than anything in Wittgenstein, though as you say, it is an analysis of a particular token of the type (“believing in”), not an analysis of the type. Quoting Wikipedia:
“According to Austin’s original exposition in How to Do Things With Words, an illocutionary act is an act:
(1) for the performance of which I must make it clear to some other person that the act is performed (Austin speaks of the ‘securing of uptake’), and
(2) the performance of which involves the production of what Austin calls ‘conventional consequences’ as, e.g., rights, commitments, or obligations (Austin 1975, 116f., 121, 139).”
Your model of “believing in” is essentially an unpacking of the “conventional consequences” produced by using the locution in various contexts. I think it is a good unpacking, too!
I do think that some of the contrasts you draw (belief vs. believing in) would work equally well (and with more generality) as contrasts between beliefs and illocutionary acts, though.
I think the kind of sensible goalpost-moving you are describing should be understood as run-of-the-mill conceptual fragmentation, which is ubiquitous in science. As scientific communities learn more about the structure of complex domains (often in parallel across disciplinary boundaries), numerous distinct (but related) concepts become associated with particular conceptual labels (this is just a special case of how polysemy works generally). This has already happened with scientific concepts like gene, species, memory, health, attention and many more.
In this case, it is clear to me that there are important senses of the term “general” which modern AI satisfies the criteria for. You made that point persuasively in this post. However, it is also clear that there are important senses of the term “general” which modern AI does not satisfy the criteria for. Steven Byrnes made that point persuasively in his response. So far as I can tell you will agree with this.
If we all agree with the above, the most important thing is to disambiguate the sense of the term being invoked when applying it in reasoning about AI. Then, we can figure out whether the source of our disagreements is about semantics (which label we prefer for a shared concept) or substance (which concept is actually appropriate for supporting the inferences we are making).
What are good discourse norms for disambiguation? An intuitively appealing option is to coin new terms for variants of umbrella concepts. This may work in academic settings, but the familiar terms are always going to have a kind of magnetic pull in informal discourse. As such, I think communities like this one should rather strive to define terms wherever possible and approach discussions with a pluralistic stance.