Embeddings are generated by neural networks, so yes, I would consider them as AI
Vector search embeddings are only as good as the models you use, the content you have, and the questions you ask.
This is a bit of a pitfall when you use them for search. Especially if you have mobile users because most of them are not going to thumb in full sentences in a search box. I.e. the questions the ask are going to be a few letters or words at best and not have a lot of context. And users will still expect good results. Vector search is not great for those type of use cases because there just isn't a whole lot of semantics in these short queries. Sometimes, all you need is just a simple prefix search.