### 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)

"All dependencies are met but the task instance is not running. In most "
                "cases this just means that the task will probably be scheduled soon "
                "unless:<br>\n- The scheduler is down or under heavy load<br>\n{}\n"
                "<br>\nIf this task instance does not start soon please contact your "
                "Airflow administrator for assistance.".format(
                    "- This task instance already ran and had it's state changed manually "
                    "(e.g. cleared in the UI)<br>"
                    if ti and ti.state == State.NONE
                    else ""
                ),
            )
        ]
        
        if ti is None:
            failed_dep_reasons: list[tuple[str, str]] = []
        else:
            dep_context = DepContext(SCHEDULER_QUEUED_DEPS)
            failed_dep_reasons = [
                (dep.dep_name, dep.reason) for dep in ti.get_failed_dep_statuses(dep_context=dep_context)
            ]
        title = "Task Instance Details"
        return self.render_template(
            "airflow/task.html",
            task_attrs=task_attrs,
            ti_attrs=ti_attrs,
            failed_dep_reasons=failed_dep_reasons or no_failed_deps_result,
            task_id=task_id,
            execution_date=execution_date,
            map_index=map_index,
            special_attrs_rendered=special_attrs_rendered,