That’s an aqua source. Needle nose will pull it out. You have already pulled the brass bonnet. It rebuilds just like a delta. And delta parts might fix it. Aqua source is old outdated delta patents. Trim is what it is. Not much choice. I would expand hole. Get a single handle valve with a 3- hole to single remodel cover. Secure it in wall and fasten the trim on. Aqua source is for house flippers. Cheap and new polished shiny chrome.