Seems possible this is not so much because ChatGPT is finding better results, but rather because it has already extracted info from the site for people to read. They don't need to show up in the visitor statistics to read (a summary of) the info on the site.
This seems reasonable and hard to disprove. A user that clicks away doesn't like what they see. ChatGPT can help you make that decision before hand.
How long until Sam Altman provides "conversation hits" as a metric for "gpt analytics". Then inevitably "encouraged" conversation directions etc. It'll come back around shortly.
Then guidelines to ensure you site is included in the model and then businesses to help optimize your site to make sure the AI models prefer your product over competitors.
Totally expected -- that is the best way to show businesses the value (and then start charging for it) -- there is NO way that they can scale a free tier without running ads.
There just isn't anywhere near enough data in this post to make any conclusions at all, especially about click conversations, which are notoriously fickle.