I was finally able to disconnect after deleting the Codex installation from GitHub, removing my Codex environments, logging out of both ChatGPT and GitHub, and clearing all cookies from my browser.
Ultimately, this allowed me to disconnect successfully. I also encountered an issue while setting up Codex with GitHub, as my repository was empty. To configure Codex with GitHub, you must commit at least one file to the repository. Codex did not provide this solution, but ChatGPT did.