Good question! I can actually check that. Let me look at what sessions are stored locally.
Yes — your conversations are stored locally. I can see 127 sessions on your machine, including recent ones like "Hugging Face successful collaborations history" and "LangChain trace sharing on Hugging Face."
So the transcripts live on your computer, not in the cloud. I can even read back the transcript of any past session if you want to revisit one.