Update docs for browser extension to reflect private code on Cloud instead of self-hosted.

Created by: quinnkeast

On the docs page linked to from the Github hovers for private code (#17264), we describe how to set Sourcegraph up for self-hosted use. With private code, Cloud users no longer need to do this. These docs will need to be updated to reflect private code on Cloud.

https://docs.sourcegraph.com/integration/browser_extension#make-it-work-for-private-code