supabase / supabase / 22197874753

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feat(assistant): send user feedback to Braintrust traces (#43021)

- Expose Braintrust span ID to client via `x-braintrust-span-id`
response header, captured in chat transport
- On feedback submission, call `logFeedback()` with `scores["User
Rating"]` (1/0), `comment`, and on the root span assign
`metadata.feedbackCategory`
- Silently skipped when tracing is disabled (HIPAA, missing env vars)
- Log `requestedModel` in trace metadata so we can see what model the
user selected vs what was actually used after throttling

Example traces:

- [Thumbs
up](https://www.braintrust.dev/app/supabase.io/p/Assistant/trace?object_type=project_logs&object_id=5a8d02e5-b3b6-40cc-ba76-ecee286478f4&r=0bb71680-784c-45c1-a234-cba0242562d6&s=0bb71680-784c-45c1-a234-cba0242562d6)
- [Thumbs down + negative
feedback](https://www.braintrust.dev/app/supabase.io/p/Assistant/trace?object_type=project_logs&object_id=5a8d02e5-b3b6-40cc-ba76-ecee286478f4&r=d5a78084-6c9a-4230-8615-1e864bb9bac7&s=d5a78084-6c9a-4230-8615-1e864bb9bac7)

<img width="645" height="173" alt="CleanShot 2026-02-19 at 13 30 25@2x"
src="https://github.com/user-attachments/assets/6c463e83-27c6-4afb-a8d0-a329ed61270a"
/>

Closes AI-442

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