Is there an euqation like quad_over_lin, but for ||x||/y, x is a vector and y is a scalar number

That in general is neither convex nor concave, even if x is a scalar and y is a scalar restricted to > 0.

If it is used in such a way that you can multiply through by y and then be in compliance with CVX’s rules, then do that; otherwise, I think you are out of luck.