Okay, I was mistaken. The tooling I was speaking of uses Claude Code rather than the SDK. One uses the Zed ACP protocol. I'm not sure about the other. I should have said Claude Code rather than the SDK. For example, I can run a session through one of the tools, and then access that session directly in Claude Code. It's still Claude though. It seems the important element is that you're not using OAuth tokens from a sub to use in a different tool. If you go through Claude Code, then Claude Code is handling everything and giving your tool the output. Thanks for the correction.