Momentum operator in QM - scalar or vector?

Momentum is a vector operator. Period.

When restricted to one-dimensional problems, momentum becomes a one-dimensional vector, which coincides with scalars in that space.

$-ihbar frac{d}{dx}$, a scalar, is the position space representation of $hat{p}_x$, the $x$ component of the momentum operator, a scalar. The momentum operator itself, $hat{textbf{p}}$, is a vector operator. The position space representation of $hat{textbf{p}}$ would be $-ihbar nabla$, a vector.

Again, the momentum operator is a vector operator. The components of the momentum operator are scalars operators.