feat: rewrite Zeebe API auth guide

[pepopowitz]

Description

Part of #4117, and resolves #4092.

Rewrites the (deprecated) Zeebe REST API authentication guide according to specs defined in #4117.

When should this change go live?

• This is a bug fix, security concern, or something that needs urgent release support.
• This is already available but undocumented and should be released within a week.
• This on a specific schedule and the assignee will coordinate a release with the DevEx team. (apply hold label or convert to draft PR)
• This is part of a scheduled alpha or minor. (apply alpha or minor label)
• There is no urgency with this change and can be released at any time.

PR Checklist

• My changes are for an already released minor and are in /versioned_docs directory.
• My changes are for the next minor and are in /docs directory (aka /next/).

• My changes require an Engineering review, and I've assigned the Engineering DRI or delegate.
• My changes require a technical writer review, and I've assigned @camunda/tech-writers as a reviewer.

[christinaausley]

This looks great @pepopowitz -- nice endurance with these! 🥳

[pepopowitz]

My apologies reviewers, I missed the fact that I'd broken two links from copypasta 😬

If you wouldn't mind, another review/approval at your convenience would be delightful.