Browser extension onboarding flow

Created by: jjinnii

Feature request description

Improve the browser extension onboarding journey for our 3 user personas:

1. Individual developers who do not have a Cloud account
2. Users with a Cloud account
3. Users using a private Sourcegraph instance

Onboarding for users should encompass:

• Authentication (for Cloud users) or validating a private instance URL
• Communicating when a private repo is not supported
  • Instructions for syncing & managing private repositories

Plan

• Create screen flow current state onboarding journey for our user types
• Identify user problems. Come to an agreement on goal/definition for a "better" onboarding flow based on our current state
• Work on visual design

Is your feature request related to a problem? If so, please describe.

Our banners and CTAs for the browser extension were created before private repositories were available on Cloud. There is a need to document the user journey for our various personas to understand how our existing flow is or is not helping users to onboard.

More to be added after user journey.

Additional context

Related issue #31843 for updating user documentation and post-installation page.