Refactor of API landing page

What does this MR do?

Ports https://gitlab.com/gitlab-org/gitlab-ce/merge_requests/25076 with EE-specific information also.

Aims to make the API landing page (currently: https://docs.gitlab.com/ee/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-ce/merge_requests/25076

Review checklist

• PM's review (recommended, but not a blocker)
• Technical writer's review (required)
• Merge the EE-MR first, CE-MR afterwards (https://gitlab.com/gitlab-org/gitlab-ce/merge_requests/25076)