It is possible that the divide here between 'applied' math and pure math is going to give you rather different results. By the nature of pure math and the academic dynamics of the field there is little benefit in bypassing publications through twitter, the fragmentation of subdisciplines makes it so that it is easier to directly reach the authors and ask for clarifications if there is something that is hard to follow.
The format of microblogging makes it hard too to express your ideas in good form, I find it personally a bit annoying having to read 20 tweet threads that are trying to approach a complex idea.
There is however a (pure) math twitter sphere that you can run into effortlessly if you start following the more well known people, but the vibe is definitely different from what Ive seen in sciences where people seem to use twitter as an extension of their academic selves. Math twitter, or the one I knew and participated in, seems to be a rather specific demographic who happen to just share their interest for math, so while some people do use it to plug their research this seems to be far from the general interest. It is not professional because pure math people are rather casual in academic settings, there is very little protocol compared to other areas.
Applied math twitter on the other hand it likely behaves more like the sciences, I have no doubt in my mind there are ML circles that would feel more familiar to the academic twitter user.
Just my two cents.