OpenAI deletes the option to publish conversations to search engines because it 'introduced too many opportunities for folks to accidentally share things they didn't intend to,' it says.

OpenAI is seemingly also solely responsible for removing the chats, perhaps most quickly by using a tool that Google provides to block pages from appearing in search results. But that tool does not stop pages from being indexed by other search engines, so it's possible chats will disappear sooner in Google results than other search engines.