As far as I understand it, in REST published_scope is just for the POS and published_at is just for the online store sales channel.
In GraphQL terms, if published_scope=global you would pass the publicationId for the POS channel. The publicationId is unique to a store but you can find is by looking for the one that has the app ID equal to 129785.
(One thing we ran into, if a store uninstall the POS app this publication will not exist on the store)
If published_at is set in REST, the equivalent in GraphQL would be to pass the publicationId of the publication that has the app ID equal to 580111 (online store).
Hope this helps some, let me know if you have any followup questions.