It wouldn't surprise me if they try, but ironically if GPT is a good personal shopper, it might make it harder to monetize with ads because people will trust the bot's organic responses more than the ads.

You could override its suggestions with paid ones, or nerf the bot's shopping abilities so it doesn't overshadow the sponsors, but that will destroy trust in the product in a very competitive industry.

You could put user-targeted ads on the site not necessarily related to the current query, like ads you would see on Facebook, but if the bot is really such a good personal shopper, people are literally at a ChatGPT prompt when they see the ads and will use it to comparison shop.