Google is already building a rival product. IIRC last year they showcased it during their hardware event. It is doing what ChatGPT does, but is targetted explicitly at answering questions and giving advice, instead of trying to converse. They said it wasn't ready at that point and likely they are facing exactly the same trouble ChatGPT does, e.g. the model confidently making stuff up.
I have no idea about the internals at google, but that seems to me a very likely direction to go. I could imagine AI generated answers as a first result in Google searches, with a promp for further user interactivity.
To be honest I am actually surprised that they got caught of guard by this. They have AI technology with similar capabilities to ChatGPT and I suspected they knew that people aren't interested in a wall of links to terrible websites, but actually want an answer to their question.