'q doctor' asking for `q login`

### 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 26.0.1 (25A362)

### Expected behaviour

i'm facing `q login` issue. but i'm unable to analyse because `q doctor` doesn't work without logging in.

### Actual behaviour

`q doctor` should work irrespective of user has logged in or not.

### Steps to reproduce

`q doctor` run it without logging into `q login`

### Environment

```yaml

[q-details]
version = "1.18.1"
hash = "a46a9baa79edc62d59b078f95d46760d0c68d6c4"
date = "2025-10-13T23:05:39.763695Z (3d ago)"
variant = "full"

[system-info]
os = "macOS 26.0.1 (25A362)"
chip = "Apple M1 Pro"
total-cores = 8
memory = "16.00 GB"

[environment]
cwd = "/Users/USER"
cli-path = "/Users/USER"
os = "Mac"
shell-path = "/bin/zsh"
shell-version = "5.9"
terminal = "iTerm 2"
install-method = "unknown"

[env-vars]
DISPLAY = "/private/tmp/com.apple.launchd.X5yPy2qlNv/org.xquartz:0"
PATH = "/opt/homebrew/share/google-cloud-sdk/bin:/Library/Java/JavaVirtualMachines/jdk-11.0.14.jdk/Contents/Home/bin:/Library/Java/JavaVirtualMachines/jdk-11.0.14.jdk/Contents/Home/bin:/Library/Java/JavaVirtualMachines/jdk-11.0.14.jdk/Contents/Home/bin/java:/opt/homebrew/opt/postgresql@16/bin:/Users/USER/.codeium/windsurf/bin:/opt/homebrew/opt/openjdk@17/bin:/Users/USER/.cargo/bin:/opt/homebrew/opt/jpeg/bin:/opt/homebrew/opt/openssl@3.0/bin:/Users/USER/.deno/bin:/Users/USER/.yarn/bin:/Users/USER/.config/yarn/global/node_modules/.bin:/Users/USER/.nvm/versions/node/v24.2.0/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:/opt/X11/bin:/Library/Apple/usr/bin:/usr/local/go/bin:/Applications/iTerm.app/Contents/Resources/utilities:/Users/USER/.local/bin:/Users/USER/.orbstack/bin:/opt/homebrew/opt/fzf/bin:/Users/USER/go/bin:/Users/USER/Library/Android/sdk/cmdline-tools/latest/bin:/Users/USER/Library/Android/sdk/platform-toolsexport"
QTERM_SESSION_ID = "1959b82a89fd4c35b6ad8e67fbf7a1f4"
Q_SET_PARENT_CHECK = "1"
Q_TERM = "1.18.1"
SHELL = "/bin/zsh"
TERM = "xterm-256color"
__CFBundleIdentifier = "com.googlecode.iterm2"
```

Beginne am Einstiegspunkt des Befehls `q doctor` und bilde das Verhalten nach, ohne `q login` abzuschließen; vergleiche anschließend seine Authentifizierungsbehandlung mit der gemeldeten Erwartung. Als abgeschlossen gilt, dass `q doctor` in einer nicht authentifizierten Sitzung ausgeführt wird und Diagnosen meldet, während der bestehende Login-Ablauf erhalten bleibt.

Vom Indexierungsmodell aus dem Issue-Text verfasst.