Some theses, especially at the undergraduate level, are expository on existing theory rather than new contributions. There are some venues that would publish such things but they need to be at a high standard.
It is difficult for students at both the undergraduate and masters level to do research resulting in true advances, partly, at least, due to the constrained timelines for such things. It is even difficult for most students to gain sufficient insight into a small area of a field to be able to begin such explorations. Some achieve it, with the help of a good advisor and a lot of work. And some advisors are better at suggesting appropriate problems than others are.
But for research in math, as in other fields to be publishable it has to be both novel and correct. "Novel" means that it makes a valuable contribution to the literature. This is judged by reviewers and editors, however, and is known only after review. Your advisor can likely judge if what you produce is something ready for submission.
But a literal answer to your headline question is that it is "publishable" when the editor says it is publishable.
