> Are there actually any good studies that show this in a counterfactual setting? Like, do we actually know that spending time teaching maths (or, less plausibly, Latin) helps students aquire these abstract skills more than other subjects? Is this "transferability" of meta-skills a testable outcome?

We know that if you try to train someone in math (or in Latin), and they do well, then they will also do well at other things in the rest of their life. Some people would like to give the credit for that good performance to the Latin training.