Could the browser extension set some DOM attr to reflect its status

This probably only matters for Harper Glasses - but maybe other people will make even better extensions something like it in the future.

Harper Glasses wasn't trying to detect whether Harper was installed or not or enabled or not before today.

I noticed it creates a `harper-render-box` so tried detecting based on that, but it's only partial detection.

So at the moment I could add a feature to Harper Glasses to tell the user they need to install Harper for it to work, but with something more like a public API I could tell the user to enable it too.

No files, tests, or entry points are named. Start by reviewing the browser-extension integration and how Harper Glasses currently detects `harper-render-box`; clarify the status values to expose and the public DOM or API contract. Done means an external extension can distinguish whether Harper is installed and enabled.

Written by the indexing model from the issue text.