SEO for AI: is Result Tracking possible?

At the agency I work for, we spend a lot of time tracking client rankings on Google and correlating that with traffic, revenue, ROI, etc. Now it seems like we need to start tracking more than just Google SERP. Does anyone have a good way to track the frequency of a brand/website being mentioned in AI results? Is there a way to know how my business is ranking when chatGPT, Claude, or Gemini is providing the response? It's not like we can latch onto a single keyword/phrase any more, so how are we supposed to do this? Does anyone even care about doing this?