As other commenters said, graders are certainly not paid from grant money at US institutions. NSF (which funds most mathematicians in the US) would never allow it, and grants are usually much better spent getting grad students off teaching so they can get research done. Teaching assistant (TA) funding would ultimately come from the university. Sometimes it is optional, i.e, a faculty member can request a TA or grader for certain courses but does not get one automatically. Some courses, like large entry-level calculus, cannot be run without teams of TAs teaching recitations.

I'm on the math faculty at a R1 (public) university, and we've not had a budget for graders for most courses for a very long time, with the exception of e.g., very large courses. For most classes the instructor does all the grading. Grading has been a significant fraction of my time teaching, certainly much more than what I can spend on preparing lectures and other teaching-related work. Moreover, much of the time grading is giving feedback, figuring out partial credit, etc; just checking "correct" or "incorrect" is often relatively quick.

In the last couple years, my personal experience has been that (i) a very small (and possibly vanishing) fraction of students are declining to use AI, or at least use it sparingly, because they want to learn; (ii) a growing percentage are using it as a personal tutor; and (iii) some are outright outsourcing all the work. The last category is small, but if that category grows (anecdotally this seems to be the case -- I've mostly taught grad courses in the last year and don't have first-hand knowledge) then what would be the point of spending all that time grading and giving detailed written feedback?

Incidentally, many students in the second category are the type who in years past would form study groups, come to office hours, etc.; now they seem to prefer AI over humans. Some of them do seem to benefit from it, but not all. How one uses AI matters a lot, and how to help students use the tech to learn is something we have to figure out (regardless of how we feel about AI's impact on research).