Unfortunately, that only helps to display the applied template, from an asset listing or search page. To actually search it, I think you would need to add a text metadata field to every Component and then the default value could be that keyword. Iām not 100% sure that would work though, and you might even need to go as far as using triggers to set that value if and when the applied template is changed for a Component.
All that being said, does the Usage screen of the Component Template asset give you the information you are looking for?