The aesthetic includes all art, and art includes... potentially everything
The question ends up turning into "what is art?"
That is a thorny question and there's no consensus. Here are some things we can say without venturing into controversial territory:
- "Art" is a category term, not an evaluation. That is, a crappy painting is still properly called art even though it is crappy, and a poorly-executed sculpture is still art -- 100% art -- despite being a mess. It is always a mistake to say something along the lines of "that isn't art because it's done badly."
- The category "art" includes vastly more things than painting and sculpture. Trivially, it also includes music, dance, origami, poetry, movies, animations, and cartoons -- and those are just some ready examples.
- Art is intimately connected with aesthetic appreciation. Some philosophers argue that this is the heart of the most workable definition of "art," but we don't have to go quite that far. Still, the odds are that where you find one, you find the other.
Thus, without going too far outside the mainstream, we have good reason to believe that we'll find aesthetic experiences all over the place, not just among the traditional "fine arts."
So, where does it end? What's doesn't or even can't give rise to an aesthetic experience?
I can't tell you. One thing we did in Philosophy of Art was consider rival definitions of "art" to see which were more or less successful at yielding inoffensive judgments, and one of the problem cases that confounded several otherwise respectable definitions was this: a beautiful natural visa, not created by humans -- not a photograph or other representation of one, but the combination of the actual place, the specific viewing conditions, and relevant characteristics of a (typical) human observer. Basically, everything documented by the EarthPorn subreddit.
And it gets worse. I'm a computer programmer by profession, and one thing we programmers discuss semi-frequently is whether a particular chunk of code is an "elegant" solution, or is an "ugly" or "awkward" hack. The properties we're attending to in these conversations are not even visual, they are conceptual: whether the code in question engages directly with the essence of the problem in a way that is straightforward, efficient in terms of run-time computation and amount of source code, whether it causes undesirable side-effects, whether it's sturdy, etc. We don't usually discuss whether it's pretty, but any programmer who has written some elegant code can tell you it has a kind of beauty of which they are proud.
I suspect the truth is that any experience can give rise to an aesthetic experience if the person living through it is in the right frame of mind. I once saw a movie where the hero was about to be tortured by the bad guy, and the hero commented on the "poetry" of their role-reversal (they had a complicated history). I could imagine that if such a scene were to play out in real life, and if the subject of the torture reflected in a similar way, that would be an aesthetic experience.