"Cupcakes in London" is not a good example since it's directly asking for advertising. Ads in more information-oriented prompts would be much easier to spot, for example looking for out of context brands and products.
That's almost certainly illegal in many jurisdictions, and they'd definitely not be able to hide that they're doing it indefinitely. A sure way to be massively sued.
Sounds like a good fit for a small, on-device model. Can Chrome extensions use the new Prompt API, which has caused a stir because Google pushed it through against opposition of virtually everyone else? (https://developer.chrome.com/docs/ai/prompt-api)
Would be hilarious.