FrankYang0529 opened a new pull request, #73032:
URL: https://github.com/apache/airflow/pull/73032

   ## Why
   
   - The scheduler recomputes `DagModel.exceeds_max_non_backfill` when a Dag 
run finishes, but only for `scheduled`, `manual` and `asset_triggered` runs. 
The flag itself counts every active run except backfill runs.
   - `asset_materialization` (#62276) and `operator_triggered` (#63733) came 
after #60006 introduced that list, and were never added to it.
   - When one of these runs is the last active run of a Dag at its 
`max_active_runs` limit, the flag stays `True` after the run finishes. The 
scheduler skips the Dag until the Dag processor parses the file again, so 
scheduled and asset-triggered runs start late.
   
   ## How
   
   - Recompute the flag for every finished run except backfill runs, which 
matches what the flag counts.
   
   ## Verification
   
   - Unit test: `breeze run pytest 
airflow-core/tests/unit/jobs/test_scheduler_job.py`
   - Integration test:
   
   1. Setup
   
   ```sh
   mkdir -p files/dags
   cat > files/dags/demo_dags.py <<'EOF'
   from __future__ import annotations
   
   import datetime
   
   from airflow.providers.standard.operators.bash import BashOperator
   from airflow.providers.standard.operators.trigger_dagrun import 
TriggerDagRunOperator
   from airflow.sdk import DAG
   
   START = datetime.datetime(2026, 1, 1, tzinfo=datetime.timezone.utc)
   
   with DAG(dag_id="demo_child", schedule="* * * * *", start_date=START, 
catchup=False, max_active_runs=1):
       BashOperator(task_id="work", bash_command="sleep 60")
   
   with DAG(dag_id="demo_parent", schedule=None, start_date=START, 
catchup=False):
       TriggerDagRunOperator(
           task_id="trigger_child",
           trigger_dag_id="demo_child",
           trigger_run_id="triggered_by_parent",
       )
   EOF
   ```
   
   2. Start Airflow
   
   ```sh
   breeze shell --backend sqlite
   ```
   
   ```sh
   export AIRFLOW__DATABASE__SQL_ALCHEMY_CONN=sqlite:////tmp/demo.db
   export AIRFLOW__CORE__LOAD_EXAMPLES=False
   export AIRFLOW__DAG_PROCESSOR__MIN_FILE_PROCESS_INTERVAL=600
   airflow standalone > /tmp/standalone.log 2>&1 &
   ```
   
   3. Trigger Dag
   
   ```
   airflow dags list
   airflow dags unpause demo_parent
   airflow dags unpause demo_child
   ```
   
   Run this until a `scheduled__...` run is `running`:
   
   ```bash
   airflow dags list-runs demo_child
   ```
   
   Trigger `demo_parent`. Its run of `demo_child` queues behind the running 
scheduled run.
   
   ```bash
   airflow dags trigger demo_parent
   ```
   
   On main branch, after `triggered_by_parent` is `success`, the next run is 
not scheduled on the next minute. The scheduler skips `demo_child` until the 
Dag processor parses the file again.
   
   ```text
   dag_id     | run_id                 | state   | run_after             | 
logical_date           | start_date            | end_date
   
===========+========================+=========+=======================+========================+=======================+========================
   demo_child | scheduled__2026-09-12T | success | 2026-09-12T11:35:00+0 | 
2026-09-12T11:35:00+00 | 2026-09-12T11:35:42.6 | 2026-09-12T11:36:43.762
              | 11:35:00+00:00         |         | 0:00                  | :00  
                  | 14960+00:00           | 543+00:00
   demo_child | triggered_by_parent    | success | 2026-09-12T11:26:17.9 | 
2026-09-12T11:26:17.76 | 2026-09-12T11:27:02.6 | 2026-09-12T11:28:03.737
              |                        |         | 12138+00:00           | 
8602+00:00             | 28857+00:00           | 794+00:00
   demo_child | scheduled__2026-09-12T | success | 2026-09-12T11:25:00+0 | 
2026-09-12T11:25:00+00 | 2026-09-12T11:25:58.5 | 2026-09-12T11:27:01.604
              | 11:25:00+00:00         |         | 0:00                  | :00  
                  | 15063+00:00           | 410+00:00
   ```
   
   On this branch, the next run is scheduled as expected.
   
   ```text
   dag_id     | run_id                 | state   | run_after             | 
logical_date           | start_date            | end_date
   
===========+========================+=========+=======================+========================+=======================+========================
   demo_child | scheduled__2026-09-12T | success | 2026-09-12T12:17:00+0 | 
2026-09-12T12:17:00+00 | 2026-09-12T12:18:17.1 | 2026-09-12T12:19:18.314
              | 12:17:00+00:00         |         | 0:00                  | :00  
                  | 51901+00:00           | 029+00:00
   demo_child | triggered_by_parent    | success | 2026-09-12T12:16:44.2 | 
2026-09-12T12:16:44.10 | 2026-09-12T12:17:14.9 | 2026-09-12T12:18:16.125
              |                        |         | 88514+00:00           | 
9705+00:00             | 91149+00:00           | 626+00:00
   demo_child | scheduled__2026-09-12T | success | 2026-09-12T12:16:00+0 | 
2026-09-12T12:16:00+00 | 2026-09-12T12:16:11.0 | 2026-09-12T12:17:13.975
              | 12:16:00+00:00         |         | 0:00                  | :00  
                  | 11254+00:00           | 608+00:00
   ```
    <!-- SPDX-License-Identifier: Apache-2.0
         https://www.apache.org/licenses/LICENSE-2.0 -->
   
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