Submit a long-running Perplexity Sonar request (e.g. sonar-deep-research) as a background async job and poll it to completion.

Documented steps

1. POST to https://api.perplexity.ai/v1/async/sonar with body {"request": {"model": "sonar-deep-research", "messages": [...]}, "idempotency_key": "<optional string>"} — request wraps a normal chat-completions-shaped payload (https://docs.perplexity.ai/api-reference/async-chat-completions-post).
2. Read back {id, model, created_at, status: "CREATED", ...} from the response and store id (the request_id) for polling.
3. Poll GET https://api.perplexity.ai/async/chat/completions/{request_id} with the same Authorization header until status moves past CREATED/IN_PROGRESS (https://docs.perplexity.ai/api-reference/async-chat-completions-request_id-get).
4. Status values are exactly CREATED, IN_PROGRESS, COMPLETED, FAILED; the full answer only appears in the response field once status is COMPLETED.
5. On FAILED, read error_message for the failure reason instead of the (null) response field.
6. To list/audit all outstanding async jobs for the account, GET https://api.perplexity.ai/v1/async/sonar, which returns a requests[] array plus a next_token cursor for pagination (https://docs.perplexity.ai/api-reference/async-sonar-get).
7. Use idempotency_key on submit to avoid double-billing if a client retries the POST after a network timeout.