Scholarships are also available at Div 2 and NAIA schools. Sports other than the headcount sports CAN have full scholarships, although they are more rare (up to the coach how to split them).
My daughter went to a D2 school and had basically a full scholarship when her athletic scholarship was combined with merit scholarships. I know a guy who had a half scholarship for lacrosse for years 1 and 2 but was promised a full scholarship for years 3 and 4 (and because of Covid, turned into year 5 too) and the coach was thrilled to ‘pay that price’ for him, because he is that good.