Just do what Kagi does and turn on AI mode only if there's a "?" At the end of the query.

They are already doing something like that though. It's not just a ? mark, but they are getting some signal from the input and classifying it as a search term or AI prompt. Not all inputs have an AI response.

And a "?" at the end is not going to capture a lot of real LLM prompts like "What should I pack for my vaction? Im going to Florida in September."

I mean you could do something like this. But it's really not much different than other manual search codes that are used by more power users like like "", "site:" etc.

They probably have a term for it but their AI response is just another "embedded result" for lack of a better term. Like displaying the local weather directly at the top when you search "weather", etc.