The state of a run is stored in the sys/state attribute. However, this is a special attribute and is currently not exposed in the Runs table, so it cannot be used as a filter.
Instead, you can sort the table by the sys/ping_time attribute. This attribute stores when the Python client last interacted with the run, and sorting by it should result in currently active runs at the top of the table.
If this solution does not work for you and you would rather have a native filter for active runs, please upvote for the feature in our feedback center.
Don't hesitate to contact support if you have a very specific requirement.