feat: Send x-session-affinity and x-parent-session-id headers

[kflansburg]

Issue for this PR

Closes #12930

Type of change

• Bug fix
• New feature
• Refactor / code improvement
• Documentation

What does this PR do?

This change adds a header that allows all providers to correlate requests across sessions (x-session-affinity). It also adds a header for requests related to sub-agent sessions that indicate the parent session id (x-parent-session-id).

How did you verify your code works?

• Ran bun test locally.
• Ran with bun run and confirmed the provider received the header.

Screenshots / recordings

N/A

Checklist

• I have tested my changes locally
• I have not included unrelated changes in this PR

If you do not follow this template your PR will be automatically rejected.

[github-actions]

The following comment was made by an LLM, it may be inaccurate:

Based on my search, I found a potentially related PR:

PR #12932 - feat: send x-session-id and x-parent-session-id headers in LLM API requests
#12932

This PR appears to be very similar to the current PR #20744. Both are about sending session-related headers (x-parent-session-id) to track session relationships in LLM API requests. The main difference seems to be that PR #12932 mentions x-session-id while the current PR uses x-session-affinity, but they're addressing the same fundamental goal of correlating requests across sessions and indicating parent-child session relationships.

You should verify the current state and scope of PR #12932 to ensure there's no duplication of effort.