Understood! Unfortunately, right now there is no way around it, the user would need to manually remove the filter using the “Clear All” button after each search. Building filters outside of the table is also an option, to be able to store and control the filters locally and remove them automatically after a search is finished, but I understand not wanting to clutter the UI as well.
This is passed on internally as a feature request which has come from the Community, to be able to control these toolbar settings for a table from an action or other external context.
Rhys