The demo flow doesn't work indicating that the extension isn't actually doing anything

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**Describe the bug**
https://blog.cloudflare.com/privacy-pass-standard/#demo-time
https://demo-pat.research.cloudflare.com/login says "Privacy Pass Token 🛑 not presented" and doesn't direct me anywhere.

**How to reproduce**
Steps to reproduce the behavior:
1. Install the extension
1. Go to https://demo-pat.research.cloudflare.com/login

**Expected behavior**
I am redirected to https://pp-attester-turnstile.research.cloudflare.com/challenge, upon solving which I see "Privacy Pass Token Valid" when visiting https://demo-pat.research.cloudflare.com/login.

**System (please complete the following information):**
- OS Windows 10 22H2
- Attesters configuration from extension options
```
https://pp-attester-turnstile.research.cloudflare.com
https://pp-attester-turnstile-dev.research.cloudflare.com
```
- Browser Helium (Chromium)
- Browser Version 151.0.7922.173
- Silk Version 4.0.2

**Additional context**
Manually going to https://pp-attester-turnstile.research.cloudflare.com/challenge and solving the challenge doesn't change anything: the demo page still says "not presented".
I've tried setting configuration to both Production and Development.

Reproduce the flow at https://demo-pat.research.cloudflare.com/login with the listed attester configuration, then try the linked challenge URL and compare production with development settings. Done means the login redirects to the challenge and subsequently reports “Privacy Pass Token Valid” after the challenge is solved.

Written by the indexing model from the issue text.