Yes, neural networks are, usually, AI, but no, thermostats are not AI.
The definition of AI is more or less "a machine that can accomplish something that an intelligent thing like a human can do but which would be unfeasible or impossible to create an explicit algorithm for the machine to follow in order to accomplish it."
So natural language translation is AI: before it became usable in the 2000s, this was seen as something that only humans could do. Producing meaningful text and recognisable images from scratch or a prompt is AI for the same reason.
On the threadiverse people equate AI with Artificial General Intelligence, i.e. something capable of true reasoning, with something we might call "understanding" (not a concept that I can attempt to define, but if you think about that ability which LLMs lack in spite of being able to produce text as if they had it) but this is ahistorical.
Interesting!
Due to the influence of Tasting History (Max Miller), this year I bought long pepper for use in a few recipes (currently marinating some shawarma) - that's an interesting flavour, also a bit sweeter (dried) than (dried) round pepper.