Hi,
I assume this “gallery action” is a custom thing defined somewhere in the envira gallery? Is that the pop-up window, that opens when you click an image in the gallery?
I’m afraid that is not possible without major modifications, as it is a feature directly implemented into the other plugin. To make that work, probably some aspects from the envira gallery output have to be applied to the results output – as well as a custom script to attach the same events to the search results to trigger the pop-up window as if it was an envira gallery item.
I am not sure how difficult this might be, but Envira gallery sure is a great plugin, so they probably do have a documentation or a guide for this somewhere. For customization works I don’t have direct contacts, but I usually recommend Envato Studio, where you can look up developers for custom jobs.