No, I don't think they are. They have enough internal smarts to replicate, and their core business has a huge buttress. That said, I wouldn't be surprised if Google makes a LOT of noise about erroneous ChatGPT results: if you could magnify a competitor mistake then why not?

Scared is an odd concept. A reaction from Google does not have to mean they are scared: if overall market and traffic size increases, even declining market share can be a relative measure against total revenue growth (I do expect some revenue fall from search but not necessarily because of ChatGPT. The worldwide economy is flat: people buy less, and so search less for things which cost money to acquire which is what paid search placement depends on for revenue)