Start with what is measurable. In your analytics tool, build a segment for referral hosts belonging to AI products and watch it as its own channel. Most default channel groupings bucket these into generic referral or even direct, so unless you define the segment yourself you will not see it.
Your server logs are the second, richer source — and they show something analytics cannot: the crawlers. AI systems fetch your pages with identifiable user agents, and the volume of those fetches is a demand signal in its own right (someone's question caused a retrieval of your page). Verifying those user agents against the vendors' published IP ranges matters, because a user-agent string alone is trivially spoofed.
Then accept the blind spot honestly. When an engine answers a question using your content and the user is satisfied without clicking, you got the influence and none of the attribution. This is the structural reason click-based analytics underreports AI impact, and why measuring whether you are named in answers is a separate, necessary instrument.
Putting it together: AI referral clicks tell you about traffic; verified crawler hits tell you about retrieval demand; answer-level visibility measurement tells you about the part where the decision actually happens. Any one of the three alone gives a distorted picture.