So what‘s your argument here? 160 search queries per second is very impressive. These aren‘t request to a stupid api, but users actually using a tool.
You could guesstimate DAU from qps by choosing a "queries per day" number (e.g., 10?) and assume the queries are done over just 8 hours. That's 1.25 queries per hour per user. Multiplying these terms out, you get ~500k DAU.
Billions of searches per year is just a weird metric that obscures what you'd actually want to know.