Implement REST API for Duo Chat

What does this MR do and why?

Add a feature-flagged REST API for Duo Chat. By allowing developers to programmatically interact with the chat, we enable them to iterate faster and conduct repeatable experiments with more ease. It also makes progress in reaching parity with the GraphQL API.

Closes #426619 (closed)

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Before	After

How to set up and validate locally

Numbered steps to set up and validate the change are strongly suggested.

MR acceptance checklist

This checklist encourages us to confirm any changes have been analyzed to reduce risks in quality, performance, reliability, security, and maintainability.

• I have evaluated the MR acceptance checklist for this MR.

Status

Blocked on !135168 (merged), which itself is waiting on !134752 (merged)