Support both GitHub App logins (for regular usage) and Personal Token logins (for notifications)

- personal is needed for personal notifications
- oauth is needed for the widget to list available repos
- management for both (unauth, etc)
- docs for both (#156)

Start by reviewing the GitHub App, personal-token, OAuth, and widget repository-listing flows described in the issue, along with documentation issue #156. Map how authentication is managed for unauthenticated users and both credential types. Done means regular widget usage works with GitHub App login, notifications use a personal token, both auth modes are managed, and documentation covers them.

Written by the indexing model from the issue text.