Is Google Agent checking out on my WooCommerce store?
Look at the order. Google-Agent with no signature is Google Agent (declared). A request signed by agent.bot.goog, when the key matches, is signed and named Google. Googlebot is the search crawler, not that checkout.
Google does not sign every agent request. An unsigned one is still a declared agent, not a person, and not proof of a forged name. A normal Chrome visit with no Google-Agent token stays Human.