@olgapapodoki Before you buy any schema app, check whether you already have schema.
Most modern Shopify themes already output Product structured data on their own. Open one of your product pages, view source, and search for application/ld+json. Or just paste the URL into Googles Rich Results Test, its free and takes a minute.
You want to see exactly one Product block. If you install an app that adds schema on top of what your theme already puts out, you end up with two Product blocks describing the same page, and that is worse than having one. Conflicting data tends to get ignored rather than merged. So check first, and only reach for an app if the check comes back empty or broken.
Second thing, and this one is a real gate that nobody has mentioned yet.
Agentic Storefronts is mostly on by default, thats right, but there are conditions attached and if you miss one you are simply not in the catalog. Go to Settings, then Policies, and make sure your Terms of service, Privacy policy, and Return and refund policy are all genuinely filled in. Not the empty template stubs, real published text. Shopify requires all three before your products are eligible for ChatGPT. Its a ten minute job and its probably the highest value thing in this whole thread.
Also worth knowing that the ChatGPT channel currently needs your store to sell to buyers in the US. Your store can be based anywhere in the world, thats fine, but if you dont sell into the US you will not show up there at all.
Then go to Sales channels, then Agentic, and look at the catalog count. If that number is lower than your active product count, some products are being rejected, usually for a missing required field like brand or GTIN. That gives you an actual list to work through instead of guessing.
One more, since a couple of people above said GA4 will hide this from you. That used to be the whole story, but Shopify now has its own reporting for this. The Agentic channel has a performance view showing sessions, referrals and sales coming from AI channels. Check there before you fall back on asking customers how they found you.
On your third question, whether anyone is seeing real sales. Be a little careful with the growth numbers floating around, they look enormous mostly because the starting point was close to zero. Worth setting up properly since the setup is free and takes an afternoon, but I wouldnt move budget away from your Google and email work for it yet.