LLMs don’t have self knowledge, and it is beneficial for predicting their correctness?

Previous works have suggested / used LLMs having self knowledge, e.g., identifying/preferring their own generations [https://arxiv.org/abs/2404.13076\], or ability to predict their uncertainty [https://arxiv.org/abs/2306.13063 ]. But some papers [https://arxiv.org/html/2509.24988v1 ] claim specifically that LLMs don't have knowledge about their own correctness. Curious on everyone's intuition for what LLMs have / does not have self knowledge about, and whether this result fit your predictions.