codeintel: Mirror repository badge on new repository page

Created by: efritz

This PR covers the first checkbox on #34490 (closed). To test locally, you will need to make the following request in the API console:

mutation CreateFeatureFlag {
  createFeatureFlag(name: "new-repo-page", value: true) {
    __typename
  }
}

List of changes:

• Move massageIndexerSupportMetadata into hooks
• Rename BadgeContent to UserFacingCodeIntelligenceBadgeContent
• Rename InternalBadgeContent to InternalCodeIntelligenceBadgeContent
• Split CodeIntelligenceBadge into CodeIntelligenceBadgeContent and CodeIntelligenceBadgeMenu
• Add content component to repo redesign page

This PR has not (intentionally) change any user-facing behaviors of the current repository menu badge - just exposes internals so that we can reuse the menu contents.

Test plan

Tested storybook and app by hand.

App preview:

• Web
• Storybook

Check out the client app preview documentation to learn more.