The claim is not that all LLMs are agents, but rather that agents (which incorporate an LLM as one of their key components) are more powerful than an LLM on its own.
We don’t know how far away we are from recursive self-improvement. We might already be there to be honest; how much of the job of an LLM researcher can already be automated? It’s unclear if there’s some ceiling to what a recursively-improved GPT4.x-w/e can do though; maybe there’s a key hypothesis it will never formulate on the quest for self-improvement.
in what context? LLMs are extremely good at bridging from natural language to API calls. I dare say it’s one of the few use cases that have decisively landed on “yes, this is something LLMs are actually good at.” Maybe not five nines of reliability, but language itself doesn’t have five nines of reliability.