Refactor of API landing page

What does this MR do?

Aims to make the API landing page (currently: https://docs.gitlab.com/ce/api/README.html) more appealing and useful, with more information on the first page.

Related issues

Relates to: https://gitlab.com/gitlab-org/gitlab-ce/issues/10421.

Author's checklist

• Apply the correct labels and milestone
• Correctly apply the product badges and tiers
• Port the MR to EE (or backport from CE): https://gitlab.com/gitlab-org/gitlab-ee/merge_requests/9509

Review checklist

• Your team's review (required)
• Technical writer's review (required)
• Merge the EE-MR first (https://gitlab.com/gitlab-org/gitlab-ee/merge_requests/9509), CE-MR afterwards