Elasticsearch bulk rejection backpressure

A search-indexer consumes a Pub/Sub pull subscription and bulk-writes documents into an Elasticsearch cluster. At 16:30 num_undelivered_messages climbs from ~2k to 500k and oldest-unacked-age rises. Dashboards: worker CPU is LOW; the workers are spending most time blocked on Elasticsearch bulk calls that now return HTTP 429 (es_rejected_execution_exception) with rising frequency, ES write thread pools/queues are saturated. The workers retry the whole bulk request on 429, immediately. No deploy on the consumer side; ES is at high indexing load from a separate reindex job. How do you triage and mitigate?