I think allowing the user to choose the location is a good idea. Also I suggest adding an option of translucent floating button like the discourse-chatbot plugin.
I think adding a button on the header will make the mobile UI a little cluttered, considering there are already 4 buttons(chat, search, menu, avatar) there. I think the AI bot feature may not need to be accessed so frequently, so adding an option in the topic-creation composer is perhaps better.
IIRC, the only way to use the bot from the official AI plugin is through PM, while the chatbot plugin can be triggered by replying to it, or @ mentioning it, which I think could be more convinient.