Bought four pinatas, nothing in the pinata menu. Bought four more, nothing in the pinata menu. What's the deal here? Is there some trouble on GoG's end because I know for a fact both purchases went through.

It says in the FAQ that it can take 24 hours to show up.
https://support.gog.com/hc/en-us/articles/115004458369-Pinata-Madness-FAQ

"I bought a Piñata and can't find it, what's wrong?
Be sure to visit your Piñata hub, this is where you can view and open all your Piñatas.
Your Piñata should appear right away – but if you still don't see your Piñata, give us some time to process your order. If your Piñata does not appear after 24 hours, please contact our support team. "

I had the same problem. In my case it was due to I was on mobile device. On pc everything goes right.

Might want to mention which browsers you were using.

There's a blue post elsewhere that says this has been fixed.