If you're on an Intel Mac, here's the reason and the fix. Cost me an evening, and I found nothing online except closed bug reports with the same symptom.
The problem: The browser flow works fine. You authorize, the page confirms, Xcode acts like nothing happened, no error anywhere.
Xcode only downloads the Apple Silicon (arm64) build of its agent binaries. On Intel they can't run at all. The process meant to receive your login dies instantly with "bad CPU type in executable" and Xcode never surfaces it.
Check if this is you: file ~/Library/Developer/Xcode/CodingAssistant/Agents/claude/*/claude If it says arm64 and your Mac is Intel, that's the problem.
The fix: Open the Info.plist next to the binary. It has the exact download URL. Download the x64 build of the same version. → Claude: change darwin-arm64 to darwin-x64 in that URL. → Codex: grab codex-x86_64-apple-darwin.tar.gz from the matching rust-v release on GitHub.
Replace the binary and make it executable: chmod 755 Update the checksum in Info.plist. It's a plain SHA-512: shasum -a 512 <binary> Restart Xcode and sign in again.
Bonus (Claude Pro / Max) Run claude setup-token in Terminal, then add the token to: ~/Library/Developer/Xcode/CodingAssistant/ClaudeAgentConfig/settings.json {"env": {"CLAUDE_CODE_OAUTH_TOKEN": "your-token"}}
Pick "Authenticate with Configuration File" in the agent menu. Runs on your subscription no API key.
Heads up: an Xcode update can re-download the wrong binary, so you may have to repeat this until Apple fixes the architecture detection.