We know the chat-data chatbot is really smart. However, website visitors see a pop-up right or left which is exactly the same as the pop-ups of all 'stupid and old' chatbots (where they have bad experiences, so they do not click).

To distinguish chat-data from old chatbots, create a new kind of launcher. Similar to the user experience people now have when using LLMs like chatgpt. See an example in screenshot. This launches the iframe of chat-data.