login UI in browser infinite loops

### Checks

- [x] I have searched [github.com/aws/amazon-q-developer-cli/issues](https://github.com/aws/amazon-q-developer-cli/issues?q=) and there are no duplicates of my issue
- [x] I have run `q doctor` in the affected terminal session
- [x] I have run `q restart` and replicated the issue again

### Operating system

macOS 15.6.1 (24G90)

### Expected behaviour

in the browser the login will succeed

### Actual behaviour

in the browser the login infinite loops. but it succeeds bc q chat will work. just the UI in the browser infinite loops and appears to have failed.

### Steps to reproduce

_No response_

### Environment

```yaml

[q-details]
version = "1.15.0"
hash = "15d28e785b64cde676048734d753dbebb106cfd3"
date = "2025-09-15T16:29:08.081869Z (5h ago)"
variant = "full"

[system-info]
os = "macOS 15.6.1 (24G90)"
chip = "Apple M2 Pro"
total-cores = 12
memory = "32.00 GB"

[environment]
cwd = "/Users/USER"
cli-path = "/Users/USER"
os = "Mac"
shell-path = "/bin/zsh"
shell-version = "5.9"
terminal = "macOS"
install-method = "unknown"

[env-vars]
PATH = "/Users/USER/.toolbox/bin:/Users/USER/.local/share/mise/installs/python/3.12/bin:/Users/USER/.local/share/mise/installs/python/3.11/bin:/Users/USER/.local/share/mise/installs/python/3.10/bin:/Users/USER/.local/share/mise/installs/python/3.9/bin:/Users/USER/.local/share/mise/installs/python/3.8/bin:/opt/homebrew/bin:/opt/homebrew/sbin:/usr/local/bin:/System/Cryptexes/App/usr/bin:/usr/bin:/bin:/usr/sbin:/sbin:/var/run/com.apple.security.cryptexd/codex.system/bootstrap/usr/local/bin:/var/run/com.apple.security.cryptexd/codex.system/bootstrap/usr/bin:/var/run/com.apple.security.cryptexd/codex.system/bootstrap/usr/appleinternal/bin:/Users/USER/.cargo/bin:/Users/USER/.local/bin:/Applications/Visual Studio Code.app/Contents/Resources/app/bin:/Users/USER/.toolbox/bin"
QTERM_SESSION_ID = "776593ad349c4cc1b4c82f62d6f91c74"
Q_SET_PARENT_CHECK = "1"
Q_TERM = "1.15.0"
SHELL = "/bin/zsh"
TERM = "xterm-256color"
__CFBundleIdentifier = "com.apple.Terminal"
```

Beginne damit, den Login-Ablauf mit `q restart` und `q doctor` zu reproduzieren, und vergleiche dann das Ergebnis im Browser mit dem erfolgreichen Verhalten von `q chat` unter macOS 15.6.1 mit Version 1.15.0. Als erledigt gilt die Aufgabe, wenn der Browser-Login Erfolg meldet und die Schleife beendet, während `q chat` weiterhin funktioniert.

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