Social login (Google) has no profileArn; chat fails with "profileArn is required but no profiles are available

### 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 26.3.1 (25D771280a)

### Expected behaviour

After logging in with Google (SocialGoogle), kiro-cli whoami should include a resolved Profile section (including profileArn).
Running kiro-cli chat should allow sending prompts and receiving responses normally.
Chat should work for social login users without requiring an enterprise profile configuration.

### Actual behaviour

kiro-cli whoami shows only:
Logged in with Google
Email address
No Profile section / no profileArn
kiro-cli chat --list-models succeeds and shows available models (auto).

Any attempt to send a message in kiro-cli chat fails with:

profileArn is required but no profiles are available. Please log in and select a profile.
This blocks all chat usage despite successful authentication.

### Steps to reproduce

Install latest Kiro CLI (e.g. 1.28.2):

kiro-cli update --non-interactive

Log in using Google:

kiro-cli login

Verify identity:

kiro-cli whoami

→ Shows SocialGoogle and email, but no profile

Confirm models are available:

kiro-cli chat --list-models

Start chat and send any prompt:

kiro-cli
> hello

Observe error:

profileArn is required but no profiles are available

(Optional) Attempt full reset:

kiro-cli logout
rm ~/.local/share/kiro-cli/data.sqlite3
kiro-cli login

→ Issue persists

### Environment

```yaml

[q-details]
version = "1.28.2"
hash = "27868a6e6508e32a80d15e6eba2f6adbab6c2aa7"
date = "2026-03-27T00:14:48.847531Z (23h ago)"
variant = "full"

[system-info]
os = "macOS 26.3.1 (25D771280a)"
chip = "Apple M4 Max"
total-cores = 16
memory = "48.00 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]
PATH = "/Users/USER/Downloads/google-cloud-sdk/bin:/Users/USER/.antigravity/antigravity/bin:/opt/homebrew/opt/python@3.12/libexec/bin:/opt/homebrew/opt/openjdk@21/bin:/opt/homebrew/opt/python@3.12/libexec/bin:/Users/USER/.cargo/bin:/opt/homebrew/share/google-cloud-sdk/bin:/usr/local/sbin:/usr/local/opt/maven@3.5/bin:/Users/USER/Applications/SnowSQL.app/Contents/MacOS:/Library/Frameworks/Python.framework/Versions/3.13/bin:/Library/Frameworks/Python.framework/Versions/3.13/bin:/opt/homebrew/opt/mysql-client/bin:/opt/homebrew/share/google-cloud-sdk/bin:/opt/homebrew/bin:/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/pmk/env/global/bin:/Applications/VMware Fusion.app/Contents/Public:/Applications/iTerm.app/Contents/Resources/utilities:/Users/USER/.local/bin:/Users/USER/.local/bin:/Users/USER/.local/bin"
QTERM_SESSION_ID = "3477ad1c57494c8082c86c376c4aa6c5"
Q_SET_PARENT_CHECK = "1"
Q_TERM = "1.28.2"
SHELL = "/bin/zsh"
TERM = "xterm-256color"
__CFBundleIdentifier = "com.googlecode.iterm2"
```

Beginne damit, den Ablauf durch die Einstiegspunkte login, whoami und chat von kiro-cli nachzustellen, und verwende dabei q doctor und q restart wie beschrieben; der Zurücksetzungspfad identifiziert außerdem ~/.local/share/kiro-cli/data.sqlite3. Als erledigt gilt die Aufgabe, wenn Google-Nutzer mit Social-Login einen aufgelösten Profile-Abschnitt mit profileArn in whoami sehen und in chat Prompts senden können, ohne eine Enterprise-Profilkonfiguration.

Vom Indexierungsmodell aus dem Issue-Text verfasst.