### 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)

"""Set state to running."""
        return self._set_dag_runs_to_active_state(drs, State.RUNNING)
    @provide_session
    def _set_dag_runs_to_active_state(self, drs: list[DagRun], state: str, session: Session = NEW_SESSION):
        """This routine only supports Running and Queued state."""
        try:
            count = 0
            for dr in session.query(DagRun).filter(DagRun.id.in_([dagrun.id for dagrun in drs])):
                count += 1
                if state == State.RUNNING:
                    dr.start_date = timezone.utcnow()
                dr.state = state
            session.commit()
            flash(f"{count} dag runs were set to {state}.")
        except Exception as ex:
            flash(str(ex), "error")
            flash("Failed to set state", "error")
        return redirect(self.get_default_url())
    @action(
        "set_failed",
        "Set state to 'failed'",
        "All running task instances would also be marked as failed, are you sure?",
        single=False,
    )
    @action_has_dag_edit_access
    @provide_session
    @action_logging
    def action_set_failed(self, drs: list[DagRun], session: Session = NEW_SESSION):