Is Neural Style Transfer considered supervised or unsupervised learning?
Neural style transfer is not really machine learning, but an interesting side effect/output of machine learning on image tasks. When performing neural style transfer using a pre-trained model, then a significant amount of supervised machine learning has already occurred to enable it.

The style transfer algorithm is still an example of gradient-based cost function optimisation, which it shares with many supervised and unsupervised learning algorithms.

The output of style transfer is partially a probe into what a network has learned about different levels of structure in the problem domain it has been trained on. However, its main use has been to generate images with altered/mixed aesthetics for art and entertainment.