That is, say you have a relatively complex backend mutation that needs to schedule some async work (eg sending an email after signup). With a Postgres queue, if you insert the job to send the email and then in a later part of the transaction, something fails and the transaction rollbacks, the email is never queued to be sent.
This is a really important point. I often end up using a combination of Postgres and SQS since SQS makes it easy to autoscale the job processing cluster.
In Postgres I have a transaction log table that includes columns for triggered events and the pg_current_xact_id() for the transaction. (You can also use the built in xmin of the row but then you have to worry about transaction wrap around.) Inserting into this row triggers a NOTIFY.
A background process runs in a loop. Selects all rows in the transaction table with a transaction id between the last run's xmin and the current pg_snapshot_xmin(pg_current_snapshot()). Maps those events to jobs and submits them to SQS. Records the xmin. LISTEN's to await the next NOTIFY.