ElasticsearchTaskHandler - Rework remote task log handling for the structlog era

[jason810496]

Body

Following #48491
we need also to convert ElasticsearchTaskHandler

airflow/providers/elasticsearch/src/airflow/providers/elasticsearch/log/es_task_handler.py

Line 120 in 1447705

class ElasticsearchTaskHandler(FileTaskHandler, ExternalLoggingMixin, LoggingMixin):

Committer

• I acknowledge that I am a maintainer/committer of the Apache Airflow project.

[eladkal]

Ash mentioned there is no need
#48491 (comment)