Enabling Authentication for API while sharing/embedding a chatbot

[briansoegaard]

I have built a chatbot and embedded it on a webpage. Great. Now, I want to access the bot via the API, both the Messing API to develop a messaging log for my client and the Upsert API to make my client upsert new files themselves. Thus, of course, I want to enable Authentication for the specific chatflow to protect the API.
When I do that, the bot breaks on the website, responding with an error in the chat and this error in the Render log file:
2024-09-19 10:00:50 [ERROR]: [server]: Error: Unauthorized

Isn't it possible to protect the API with authentication while embedding the bot on a webpage? It doesn't make sense, I guess?