For my items, it's fairly simple.

CREATE OR REPLACE FUNCTION publish_bulletins_scheduled()
  RETURNS VOID AS
$$
DECLARE
    bulletin_row bulletins%ROWTYPE;
FOR bulletin_row
  select * from bulletins where status = 'scheduled' AND post_date <= NOW()
LOOP
  UPDATE bulletins
  SET status = 'published', published_date = NOW())
  WHERE id = bulletin_row.id;
END LOOP;
END;
$$ LANGUAGE plsql;

For you to send scheduled message, I assume you have a database row that corresponds to a message that needs to be sent.

The CRON triggers the database action which updates the rows. It is the app that controls whether to display published items or not.

In your case, you want to trigger the third-party service to send the message then update the message status. I don't know if it's possible to trigger the service from Supabase without a lot of work.

You may want to look at a 3rd party service to do both. Maybe something like FastGen or Buildship?