Browser extensions + native integrations should support private code on dotcom (yay!)

Created by: Joelkw

The sourcegraph browser extension seems to block private code on dotcom with a PrivateRepoPublicSourcegraphError on the backend and a modal (attached) on the frontend. We should update this so:

1. Private code isn't blocked automatically with the error
2. The modal instead instructs you how to connect private code to Sourcegraph (which you can do now!) instead of instructing you to set up a private sourcegraph instance

This should be updated and released before the Cloud Launch, so by July 14 (to account for review delays). We should update our native integrations as well as all browsers' extensions.

(Note for some reason in my tests eventually the hovertooltip goes away and I do get some basic code intel hovers from Sourcegraph. I'm not sure why this is and see no console output, but we should test our updates thoroughly.)