Does sigmoid facilitate modeling non-linear decision boundaries or does this come from high-dimensional data?
The power to model non-linear decision boundaries comes directly from the non-linear activation function. You can understand this when you see that concatenating N linear transformations (i.e. dense layers) is equivalent to a single linear transformation. This is the mathematical proof with 2 linear layers:
$ y = (xW_1 + b_1) W_2 + b_2 = x W_1 W_2 + (b_1 W_2 + b_2) = x W' + b'$
(where $W'= W_1 W_2$ and $b'= b_1 W_2 + b_2$)