I've done a ton of work on this from both sides and:
• In general for crawling, almost all the AI bots are still doing HTML scraping, and not executing javascript and not loading things like image "pixels" that are used for tracking. They aren't going to show up in most marketing analytics tools like Posthog, GA, Plausible, etc. in the same way that you don't see Ahrefs+SemRush+Majestic site crawlers in those tools.
• There has been a big uptick in bot traffic (scrapers) in many cases as the the AI companies are in a frenzied landgrab of trying to get unadultered, pre-regurgitated data to build their foundational models off of.
• While you _can_ compare referrals in GA for things like AI traffic that tends to really under-report the impact of AI search ranking in ChatGPT, etc. as behaviorally they're using the AI for research and deciding what to do and then doing a navigational search or brand search in Chrome so it's being reported as "organic"