I ran into the exact same issue on an Intel Mac and was able to fix it: the problem is not the browser auth flow, but that Xcode’s CodingAssistant downloads the local codex agent in the wrong architecture (arm64 instead of x86_64), so the helper process that should receive the login result immediately crashes with bad CPU type in executable and Xcode shows no error; the fix is to go to ~/Library/Developer/Xcode/CodingAssistant/Agents/codex/<version>/, replace the wrong ARM binary with the matching Intel build extracted from the same release’s codex-x86_64-apple-darwin.tar.gz, run chmod 755 codex, update the checksum and url fields in the adjacent Info.plist using shasum -a 512 codex, then restart Xcode and sign in again.