### 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)

"""Return a list of dot-separated dictionary paths."""
    for key, value in input_dict.items():
        if isinstance(value, dict):
            for sub_key in get_key_paths(value):
                yield ".".join((key, sub_key))
        else:
            yield key
def get_value_from_path(key_path, content):
    """Return the value from a dictionary based on dot-separated path of keys."""
    elem = content
    for x in key_path.strip(".").split("."):
        try:
            x = int(x)
            elem = elem[x]
        except ValueError:
            elem = elem.get(x)
    return elem
def get_task_stats_from_query(qry):