closes: #66067

task.queued_duration (legacy: dag.<dag_id>.<task_id>.queued_duration) stopped being emitted in Airflow 3 regardless of executor (LocalExecutor, CeleryExecutor, KubernetesExecutor). The companion (LocalExecutor, CeleryExecutor, KubernetesExecutor). The companion metric task.scheduled_duration still emits.

In Airflow 2 the worker emitted task.queued_duration from TaskInstance._check_and_change_state_before_execution (airflow-core/src/airflow/models/taskinstance.py:1366) on the QUEUED → RUNNING transition. In Airflow 3 the worker no longer touches the DB directly — it reaches RUNNING through the Execution API endpoint PATCH /execution/task-instances/{id}/run (airflow-core/src/airflow/api_fastapi/execution_api/routes/task_instances.py), which never called TaskInstance.emit_state_change_metric. The companion metric kept working because the scheduler still emits task.scheduled_duration directly from scheduler_job_runner.py:990 when it queues the TI — that path was not affected by the worker/API split.

Emit task.queued_duration inline from the run endpoint on the first QUEUED → RUNNING transition. The legacy TaskInstance.emit_state_change_metric is not reused here because the handler operates on a partial-column Row (not a TI ORM instance) and the update later resets end_date to None, which would defeat the method's "only on first try" guard for retries. Mirroring the guard inline (end_date is None and queued_dttm is not None) preserves the legacy semantics — including not emitting on retries — and uses the same tag set (task_id, dag_id, queue).

Two regression tests in airflow-core/tests/unit/api_fastapi/execution_api/versions/head/test_task_instances.py:

• test_ti_run_emits_queued_duration_metric — first transition emits with the expected metric name, timing (now - queued_dttm), and tags.
• test_ti_run_skips_queued_duration_metric_on_retry — a retry (previous attempt's end_date populated) does not emit, matching legacy behavior.

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