Typically, people don't change out their browser/app. I know there is a vanguard of loyalty-fluid users out there but the reality is product inertia is real.
Myself for example, will continue to use Chrome even though I have a half dozen browsers installed for testing. So an AI augmented browser interests me about as much as an AI integrated laptop. That is not at all.
However, having said that, I think Google's biggest threat is that people can typically get better, ad free answers from chatGPT for many queries and people will switch (at least I will) to a new source of better information.