Create engagement

Creates a new `CALL` or `MEETING` engagement by ingesting either a media recording from an external URL or a structured transcript timeline. **Idempotency:** The `external_id` field is the idempotency key. Submitting the same `external_id` again — even with a different `source_system` — returns the existing engagement with a `200` response instead of creating a duplicate. If you need per-source-system uniqueness, prefix your `external_id` (e.g. `my-crm:12345`). **Recording imports:** Provide `media_url` when you want AskElephant to fetch and transcribe a recording. The URL must be a publicly accessible HTTPS URL serving an `audio/*` or `video/*` content type. HTTP URLs, private/internal IP addresses, and non-media content types are rejected with a `422` error. The server fetches the media synchronously during request processing, so the URL must remain accessible for the duration of the request. **Transcript-only imports:** If you do not have recording media, omit `media_url` and provide `transcript_timeline`. The timeline must include declared speakers plus timed transcript entries whose `speaker_index` values reference those speakers. **Workflow control:** Set `run_workflows` to `true` for normal automation (workflow triggers, recap emails) or `false` to suppress workflows (e.g. for historical imports). Transcription, summarization, and tagging always run regardless. **Owner participant:** Optionally mark exactly one participant with `is_owner: true` to assign engagement ownership to that user instead of the API-key-associated user. The marked participant must resolve to an active AskElephant user in the authenticated workspace. Resolution matches `email` first, then `phone`; users with `INACTIVE` or `NOT_INVITED` roles are not valid targets. When exactly one `is_owner: true` participant resolves successfully, the created engagement's `owner_user_id` and downstream processing use that user as owner and host. When no participant has `is_owner: true`, ownership defaults to the user associated with the API key or OAuth credential. Requests with more than one `is_owner: true` participant, or with a single owner participant that cannot resolve to an active workspace user, return HTTP `400` and do not ingest media, persist an engagement, or publish processing events. API keys or OAuth credentials without an associated user may create an engagement only when a valid explicit owner participant is provided. **Timestamps:** If `start_at` is omitted, the current server time is used. When `transcript_timeline` is provided, `end_at` is derived from the largest `transcript_timeline.entries[].end_seconds` value, even if `media_url` is also supplied. For media-only imports (no timeline), `end_at` is derived automatically from the media duration during processing. This operation requires the `engagements:write` scope.