Perhaps if it retained the follow-up questions (but perhaps a little more condensed), and it was clicking one of these that flipped you to the full chat UX, that would feel more intuitive.
It just feels like the full chat UI is being initialised a step too early - I expect a results page with my initial summary, but there is an input box at the bottom of the screen.
Perhaps you could also include a 'move to chat view' icon or link, so the same summary response can still feed into that journey as well as straight into the same UX. You could also only show the FAB-style buttons to toggle between views when someone has already initiated the 'chat from search' functionality, so it wouldn't be in the way of people who just want a summary. This way users could 'upgrade' their search to the chat toggle view, only where they want that experience.
Just some thoughts - I'm sure you have designers with better ideas than me!