### Description

Going to Airflow web UI, Browse>DAG Run displays the list of runs, but there is no way to search or filter based on the text in the "Note" column.

### Use case/motivation

It is possible to do a free text search for the "Run Id" field. The Note field may contain pieces of information that may be relevant to find, or to filter on the basis of these notes.

### Related issues

Sorting by Note in List Dag Run fails: 
https://github.com/apache/airflow/issues/30041

### Are you willing to submit a PR?

- [ ] Yes I am willing to submit a PR!

### Code of Conduct

- [X] I agree to follow this project's [Code of Conduct](https://github.com/apache/airflow/blob/main/CODE_OF_CONDUCT.md)

"max_active_runs": max_active_runs,
                }
            )
        return flask.json.jsonify(payload)
    def _mark_dagrun_state_as_failed(self, dag_id, dag_run_id, confirmed):
        if not dag_run_id:
            return {"status": "error", "message": "Invalid dag_run_id"}
        dag = get_airflow_app().dag_bag.get_dag(dag_id)
        if not dag:
            return {"status": "error", "message": f"Cannot find DAG: {dag_id}"}
        new_dag_state = set_dag_run_state_to_failed(dag=dag, run_id=dag_run_id, commit=confirmed)
        if confirmed:
            return {"status": "success", "message": f"Marked failed on {len(new_dag_state)} task instances"}
        else:
            details = [str(t) for t in new_dag_state]
            return htmlsafe_json_dumps(details, separators=(",", ":"))
    def _mark_dagrun_state_as_success(self, dag_id, dag_run_id, confirmed):
        if not dag_run_id:
            return {"status": "error", "message": "Invalid dag_run_id"}
        dag = get_airflow_app().dag_bag.get_dag(dag_id)
        if not dag:
            return {"status": "error", "message": f"Cannot find DAG: {dag_id}"}
        new_dag_state = set_dag_run_state_to_success(dag=dag, run_id=dag_run_id, commit=confirmed)
        if confirmed:
            return {"status": "success", "message": f"Marked success on {len(new_dag_state)} task instances"}
        else:
            details = [str(t) for t in new_dag_state]
            return htmlsafe_json_dumps(details, separators=(",", ":"))
    @provide_session
    def _mark_dagrun_state_as_queued(