The reason Claude looks up the docs of itself is because the model doesnt know about harness features that havent landed yet. The harness itself can be ahead of the model. Happens all the time.
Makes me wonder about doing some archaeology and trying out really old harnesses on modern models...
I don't expect the model to be trained on the latest features of the harness, but I think the harness should ship with its own docs so that the model can quickly search local docs rather than search online page by page for docs that don't necessarily match the local harness.