Aurora global database, write forwarding enabled, but still getting "read-only mode"

Write forwarding is enabled. https://docs.aws.amazon.com/AmazonRDS/latest/AuroraUserGuide/aurora-global-database-write-forwarding.html

The application is using set aurora_replica_read_consistency = 'session';

However, we're still getting "Running in read-only mode" for the secondary cluster.