The big breakthrough is we can interact with the agents using natural language - because of the LLM.
It is the combination of LLM and agent-harnesses that make it look really smart. Agent-harness is a programmatic device that lets us tap into the vast knowledge in the LLM.
It is probabaly true that many TV-commentators fail to appreciate this fact and therefore think LLMs are super-intelligent. No, it is the combination of LLM and the programmatic agent-haness that is the breakthrough.
An interesting thought is that the LLM could in theory code the agent-harrness, start it running every time we interact with it. Currently the agent-harrness I think is pretty static I think. In theory it could be dynamically created for every task. Would that make it better don't know.