The way users use Facebook and LLMs are so massively different, it almost seems like a bad faith argument to equate them.

Facebook is mostly scrolling the timeline and passive consumption. It doesn't benefit from being on the side because the content you interact with on Facebook is completely separate from the content on your other tabs.

In contrast, LLMs have ongoing conversations that the user can come back to, and each conversation might relate to multiple tabs that the user is working on. On top of that, it's a very common occurrence that the user has questions about, or a task to be done using the content of the current page. This makes LLM and chatbot integration much more useful than a Facebook integration.

Also if you have the Facebook Messenger installed, Firefox already gives you an integration to share things with your Facebook contacts.