Same gap here: a handful of ChatGPT/Perplexity sessions, almost nothing Shopify clearly calls an AI order, and customers who say they found us there showing up as Direct.
Building on what mclab said, two things that helped beyond the referrer filter:
When someone clicks through from ChatGPT search, the link often carries utm_source=chatgpt.com. Check sessions and orders by UTM source, not only the channel summary, because some of those visits get bucketed somewhere you wouldn’t look.
On the post-purchase “how did you hear about us” question, give “ChatGPT / AI assistant” its own option instead of leaving it under “Other”. After a couple of months you get a rough ratio you can apply to the Direct bucket.
Then watch branded search impressions in Search Console. If AI answers are sending people your way, more of them google your store name afterward.
Treat the AI number as directional, not exact.