Amazon login error with a ghost sesstion

### 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 15.5.0 (24F74)

### Expected behaviour

After logged in, it available to using q command to as the Model

### Actual behaviour

After login with GUI or CLI, q command cannot use and login require are spammed cuz the login operation not work properly.

### Steps to reproduce

Fresh install via homebrew -> Login Via GUI -> Use q command in terminal -> error: You are not logged in, please log in with q login -> login via CLI -> Select login method · Use for Free with Builder ID ->Device authorized,Logged in successfully -> use q command in terminal -> error: You are not logged in, please log in with q login

### Environment

```yaml
[q-details]
version = "1.12.7"
hash = "ed77799a52644ba49a3ed76b15c25cd9334c4b8d"
date = "2025-07-22T17:41:04.597455Z (13h ago)"
variant = "full"

[system-info]
os = "macOS 15.5.0 (24F74)"
chip = "Apple M2"
total-cores = 8
memory = "16.00 GB"

[environment]
cwd = "/Users/USER/Documents/code/remote/fconnect-api"
cli-path = "/Users/USER/Documents/code/remote/fconnect-api"
os = "Mac"
shell-path = "/bin/zsh"
shell-version = "5.9"
terminal = "Cursor"
install-method = "brew"

[env-vars]
PATH = "/Users/USER/.pyenv/shims:/Users/USER/.pyenv/bin:/Library/Frameworks/Python.framework/Versions/3.12/bin:/Users/USER/.nvm/versions/node/v22.11.0/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:/Applications/VMware Fusion.app/Contents/Public:/usr/local/go/bin:/Users/USER/.pyenv/bin:/Library/Frameworks/Python.framework/Versions/3.12/bin:/Users/USER/.nvm/versions/node/v22.11.0/bin:/Users/USER/.local/bin:/Users/undefined/Library/Application Support/JetBrains/Toolbox/scripts:/Users/USER/.cursor/extensions/ms-python.debugpy-2025.8.0-darwin-arm64/bundled/scripts/noConfigScripts:/Users/undefined/Library/Application Support/JetBrains/Toolbox/scripts"
QTERM_SESSION_ID = "aaf89855e44047e992fe5967a73085eb"
Q_SET_PARENT_CHECK = "1"
Q_TERM = "1.12.7"
SHELL = "/bin/zsh"
TERM = "xterm-256color"
ZDOTDIR = "/Users/USER"
__CFBundleIdentifier = "com.todesktop.230313mzl4w4u92"
```