curl --request POST \
  --url https://api.veryfront.com/conversations/{conversation_id}/branches \
  --header 'Authorization: Bearer <token>' \
  --header 'Content-Type: application/json' \
  --data '
{
  "message_id": "3c90c3cc-0d44-4b50-8888-8dd25736052a",
  "parts": [
    {
      "text": "<string>"
    }
  ]
}
'

{
  "id": "<string>",
  "conversation_id": "<string>",
  "seq": 123,
  "parts": [
    {
      "text": "<string>"
    }
  ],
  "created_at": "<string>",
  "parent_id": "<string>",
  "created_by": "<string>",
  "sender_type": "user",
  "sender_id": "<string>",
  "sender_display_name": "<string>",
  "model": "<string>",
  "token_usage": {},
  "finish_reason": "<string>",
  "cost_credits": "<string>",
  "edited_at": "<string>",
  "idempotency_key": "<string>",
  "metadata": {},
  "updated_at": "<string>"
}