After hearing this discussed on a recent coaching call, I thought I'd share my experience. Firstly, if you're on Etsy and have off-site ads turned ON, the good news is that Etsy advertises on Google for you. And you only pay if you make a sale directly from an off-site ad.
If you're on Shopify, you can use the Google sales channel. I'd say that this is definitely an Advanced stage thing to do, however, and not for beginners to worry about or anyone who isn't confident about using tech. I've found that Google's channels are the worst when it comes to using developer-speak and they can be very unintuitive.
I don't use paid Google ads, but I do use the free shopping listings - because they're free, so why not! To do any Google advertising, other than Etsy, you need a Google Merchant Center account, which the Shopify sales channel can guide you into creating if you don't already have one. I've found the Google e-com environment to be something of a learning curve, very fiddly and rather temperamental. Like Facebook, your listings can be suddenly disapproved for reasons that are not always easy to work out or fix. I've figured out some of the quirks and workarounds over time, but patience and determination are sometimes required! 😉