Pages served from service workers don't get the overriden user agent.

[jrmuizel]

Steps to reproduce:

• Override the user agent
• Load https://service-worker-user-agent.netlify.app/ (the overriden user agent shows up)
• Hit refresh. It should now say ✓ Controlled by service worker — this page can now load offline. but the user agent won't be the overridden one.

[hiSandog]

This is a useful repro because it isolates service-worker-controlled navigations. The key question is whether the extension only rewrites normal network requests and misses requests fulfilled or initiated through the service worker lifecycle after refresh. A follow-up test with DevTools showing the request initiator and headers for the first load versus the controlled refresh would make it easier to tell whether the fix belongs in request interception, service worker registration handling, or documentation of browser limitations.