I had a similar problem, so I enabled checkpoints and set the max checkpoint timeout to 60 seconds. Data started being inserted into my Iceberg table.

https://nightlies.apache.org/flink/flink-docs-release-1.20/api/python/reference/pyflink.datastream/api/pyflink.datastream.stream_execution_environment.StreamExecutionEnvironment.enable_checkpointing.html?highlight=enable_check#pyflink.datastream.stream_execution_environment.StreamExecutionEnvironment.enable_checkpointing