### 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)

"""Check if the datetime is a UTC one."""
        from airflow.utils.sqlalchemy import UtcDateTime
        if col_name in self.list_columns:
            obj = self.list_columns[col_name].type
            return (
                isinstance(obj, UtcDateTime)
                or isinstance(obj, types.TypeDecorator)
                and isinstance(obj.impl, UtcDateTime)
            )
        return False
    def is_extendedjson(self, col_name):
        """Checks if it is a special extended JSON type."""
        from airflow.utils.sqlalchemy import ExtendedJSON
        if col_name in self.list_columns:
            obj = self.list_columns[col_name].type
            return (
                isinstance(obj, ExtendedJSON)
                or isinstance(obj, types.TypeDecorator)
                and isinstance(obj.impl, ExtendedJSON)
            )
        return False
    def get_col_default(self, col_name: str) -> Any:
        if col_name not in self.list_columns:
            
            return None
        return super().get_col_default(col_name)
    filter_converter_class = AirflowFilterConverter
class DagRunCustomSQLAInterface(CustomSQLAInterface):