Multiplication is a form of repeated addition. But scaling is correct too. Scaling is to multiply by a scalar. When you multiply a scalar and a vector, the vector lengthens or contracts. This can also be repeated addition of the vector.

However, the repeated addition concept falls apart with multiplication by zero.

Sort of. Certainly 0 x 5=0 is not repeated addition.

Except 0 x 5=5 x 0=0+0+0+0+0. So it can work.