Apparently they've recently added a first party side bar for LLM integration, but I haven't tried it out yet.

Yes, that's one of the things that really should have been an extension. Tree Style Tab works alright as an extension-provided sidebar.

Putting the chat or sidebar in the core of the browser sounds very much like something done by a developer who wasn't around for Mozilla prior to Firefox, and isn't aware of the original goal of being the antithesis of the browser that included everything and the kitchen sink.