I had the same problem; what I did was log out (and yeah, trying to log out properly with Codex is a big pain—you need to remove the config files). Then follow the instructions, and after I logged in the spinner ran on the GUI. I fired up Codex in Terminal, waited a moment, and closed the spinner UI. It told me it failed, then quit Xcode and Codex, and it should then let you continue as if nothing went wrong. to install the CLi version: https://developers.openai.com/codex/cli
Of course, yesterday after I installed macOS 13.3, Xcode froze on startup, telling me it was trying to recover a document that was not saved correctly. I wiped Xcode and ~/Library/Developer, rebooted, and installed Xcode 26.3 RC; the problem was still there (?). Installing Xcode 26.2 made the problem go away. The issue must be with Codex.
Uninstalling Codex does not help either—it keeps hanging on startup—so I wiped Codex config files in ~/Library. Xcode still hung, but I could click on the menu and get a response; tapping on the “triangle” I could see that the problem persisted. Clicking on Agent Settings throws the beach ball, so I quit, and a few minutes later Xcode realized Codex wasn’t there anymore.
Given the daily Codex updates, there is probably some work to be done by Apple and OpenAI.