Verify proxy auth + config switching end-to-end in Chrome

[infralayers]

Goal

This is the project's actual v1 success criterion (see design spec): confirm the example extension works against a real proxy in Chrome, not just unit tests.

Steps

1. npm install && npm run build --workspace=packages/core && npm run build --workspace=packages/example-extension
2. Follow packages/example-extension/README.md "Load in Chrome" section
3. Enter a real proxy's host/port/username/password in the popup, click "Enable proxy"
4. Confirm the popup shows "Proxy enabled"
5. Open the service worker inspector (chrome://extensions → "service worker" link) and confirm no console errors
6. Confirm traffic actually routes through the proxy (e.g. check the proxy's own logs, or visit an IP-check site before/after enabling)

Definition of done

Comment on this issue with what you tested against and confirm it worked (or file bugs you found as new issues, linked from here).

Suggested owner: whichever of you is more comfortable with Chrome DevTools — pick one, no need to split this further.