I found an issue similar to your question that might be helpful, as it resolved the issue with Datastream from PostgreSQL to BigQuery. This suggests assigning the Superuser permission to your user and trying the query below with this documentation.

ALTER USER <the user> WITH REPLICATION;

Another troubleshooting step you could try is checking PostgreSQL Memory and Configuration; Review PostgreSQL’s memory configuration (e.g., shared_buffers, work_mem) and ensure they are appropriately set. Increase the memory limits if required to accommodate larger workloads, especially when Datastream is trying to process a high volume of changes.