I made an agent to derive and iterate on a stock trading strategy for me. What I did was give it a virtual bank account that models your typical brokerage account. So my agent reads the news, financials, markets, all the information it can gather to decide what stocks to buy/sell and manage its portfolio. Then what I do is just follow along with real money.

I could see shopping being the same way, let the agent shop for you or identify good deals on things you want but then push them to you to make the actual purchase. Like you, I'm certainly not going to let an agent make a real purchase for me unattended and I doubt any merchant is going to have much sympathy for "my AI bought this by mistake".