feat: replicate mgmt-api index

[darrickyong]

Description

This PR adds the index.mdx files for mgmt-api. It also updates the en-index.mdx to match current content.

References

Testing

Checklist

• I've read and followed CONTRIBUTING.md.
• I've tested the site build for this change locally.
• I've made appropriate docs updates for any code or config changes.
• I've coordinated with the Product Docs and/or Docs Management team about non-trivial changes.

[github-actions]

Summary

Status	Count
🔍 Total	48
✅ Successful	45
⏳ Timeouts	0
🔀 Redirected	0
👻 Excluded	3
❓ Unknown	0
🚫 Errors	0
⛔ Unsupported	0
Full Github Actions output

[mikemimik]

✋🏽 Change Request: Can you copy the english content into the French and Japanese files as well. At the moment it's okay that the content is not translated. Missing content would be a worse state.