I think we can confidently conclude that there are two or even more conflicting definitions of "sentence". Analogously, there are multiple definitions of "markedness". However, your first quote:
Generative grammar is a linguistic theory that regards grammar as a
system of rules that generates exactly those combinations of words
that form grammatical sentences in a given language.
is not a definition of "sentence", it is a claim about GG and what a grammar does does. I will leave aside the question of whether it is accurate as a characterization. If this claim is true, we might infer some definition of "sentence", but it isn't a definition.
I presume that your real question is about some claim, and not the definition of "sentence", but I'm not entirely sure what the claim in question is. The primary question, I think, is a version of the old competence / performance problem: is "what to do?" grammatical, or merely acceptable? If this string is grammatical, then (by definition) it is generated by the grammar, and the claim that (grammars only generate sentences and all sentences have subjects and verbs) is false. That is, at least one of those claims is false, possibly both. If the string is ungrammatical but acceptable, then we learn nothing about what a grammar does.
The claim that every sentence has a subject and a finite verb has a consequence, that imperatives are also not sentences. Forget that, I say. It also means that many utterances in languages without verbal copulas are not sentences. Perhaps (indeed, almost certainly), the claim was intended to be about English, not the concept "sentence", but GG is not a theory of English, it is a theory of language (despite initial appearances). We could say that the claim is not a claim about surface word order, it's a claim about logical form, so that there are always elided finite verbs or deleted subjects, but that "What to do?" would come from "What should we do?". Similarly, "Banana" could be the sort form of a number of sentences, such as "I'll have a banana" or "The English word for 'banana' is 'banana'".
There is no good way to assess the social construct of conventionality, because there's no system of opinion-polling / voting. One may reach certain surmises by looking at the literature to see what certain people say, and perhaps that it the only operationally-sensible way to talk about conventionality of concepts. Each publication is weighted according to impact factor of something like that, and if high-impact papers tend to converge on a particular conclusion, that is what counts as "conventional". I presume the problems with this approach are obvious.
