[v3-2-test] Fix: Restore live stdout logging for Elasticsearch log forwarding (#64067)#64592

eladkal merged 2 commits intov3-2-testapache/airflow:v3-2-testfrom

backport-f1495c2-v3-2-testapache/airflow:backport-f1495c2-v3-2-testCopy head branch name to clipboard