CREATE TABLE widget_conversation_contact_inbox_backfills (
  conversation_id BIGINT PRIMARY KEY,
  contact_inbox_id BIGINT NOT NULL
);

INSERT INTO widget_conversation_contact_inbox_backfills (conversation_id, contact_inbox_id)
SELECT conversations.id, MIN(contact_inboxes.id)
FROM conversations
JOIN inboxes ON inboxes.id = conversations.inbox_id
JOIN contact_inboxes
  ON contact_inboxes.contact_id = conversations.contact_id
 AND contact_inboxes.inbox_id = conversations.inbox_id
WHERE conversations.contact_inbox_id IS NULL
  AND inboxes.channel_type IN ('web_widget', 'Channel::WebWidget')
GROUP BY conversations.id
HAVING COUNT(contact_inboxes.id) = 1;

UPDATE conversations
SET contact_inbox_id = (
  SELECT backfills.contact_inbox_id
  FROM widget_conversation_contact_inbox_backfills AS backfills
  WHERE backfills.conversation_id = conversations.id
)
WHERE id IN (SELECT conversation_id FROM widget_conversation_contact_inbox_backfills);