[Fix] Update example n remove session on logout

[makylfang]

PR

Describe your changes

• Updated example
• Removing session on disconnect event

Checklist before requesting a review

• You have performed a self-review of your own code
• You are using approved terminology
• Your changes have been tested locally
• Your code builds clean without any errors or warnings

[netlify]

✅ Deploy Preview for authsdk-ref-guide ready!

Name	Link
🔨 Latest commit	5d6e668
🔍 Latest deploy log	https://app.netlify.com/sites/authsdk-ref-guide/deploys/64a27796560c5f0008a0a1f5
😎 Deploy Preview	https://deploy-preview-195--authsdk-ref-guide.netlify.app
📱 Preview on mobile	Toggle QR Code... Use your smartphone camera to open QR code link.

---

To edit notification comments on pull requests, go to your Netlify site configuration.

[netlify]

✅ Deploy Preview for dev-authsdk-ref-guide ready!

Name	Link
🔨 Latest commit	5d6e668
🔍 Latest deploy log	https://app.netlify.com/sites/dev-authsdk-ref-guide/deploys/64a27796bd58830008c92022
😎 Deploy Preview	https://deploy-preview-195--dev-authsdk-ref-guide.netlify.app
📱 Preview on mobile	Toggle QR Code... Use your smartphone camera to open QR code link.

---

To edit notification comments on pull requests, go to your Netlify site configuration.

[mmjee]

LGTM