Genuine question, is the reasoning chain different from clicking the status bar under a reply and watching it "think"? Or selecting the "Thinking" transcript view in Claude Code? (both on the desktop app). Seems to me that is very out in the open

That's a summarized and filtered view of the actual reasoning.

OpenAI and Anthropic guard the real reasoning closely. Users have never been able to see it and the API returns an encrypted blob instead of legible reasoning.