Ideally it would have to be a distributed system or take payments from users. It is to tempting for big AI platforms to avoid acting just like the shopping platforms.
The conversational commerce agent can use MCP-UI[0] to show the payment UI (Stripe Elements and Paypal Button) directly in the chat and that taps into the same payment API the shop's storefront uses.
I'm kind of building this already[1].
0. https://mcpui.dev/
1. https://marketplace.openship.org