You've noticed some
COPY commands being issued to your database in the Postgres logs
These are likely being issued by PG Backups, either through manual or scheduled backups. You can check the timestamp seen on the log entry against the backups timestamp to see if they correlate.
heroku pg:backups -a app-name will list all backups.
You can also check the timing of your scheduled backups with
heroku pg:backups:schedules -a app-name
Depending how quickly the
COPY completed you may not queries for all tables. Heroku Postgres Logs show queries that take longer than 2 seconds: https://devcenter.heroku.com/articles/postgres-logs-errors#log-duration-3-565-s