Functionally I think it could work well, shop listings are no different from posts but with a price and a buy link.

I don’t know if it would be a good idea as a few challenges immediately come to mind:

If your site hosted products from a decentralized web, how would you guard your site against bad actors or scams?

How would you be able to monitor stock?

How would you negotiate deliveries or a unified shopping cart?

How would you instill trust in a user that a product was legit and could be backed by a return or a guarantee?

How would you make sure your site maintained a perception of quality items?

For this to work, I imagine you would have to only Federate with store fronts you were actively affiliated with, ideally in your area or under the same delivery umbrella at which point you might as well have a unified store front. The decentralized aspect would probably create alot of hiccups and distrust you wouldn’t want anywhere near money changing hands.

I think a decentralized storefront would basically look a lot like AliExpress or Amazon if you went the store route, but without any big company backing or a unified delivery service. It could also be a large, even less trustworthy and hard to manage Facebook Marketplace or Gumtree. It wouldn’t survive long.

What could work though is if you were partnered with a bunch of individual, small stores that each were making a name for themselves within a similar space. Their stores could feed products to a larger store that users could search and browse in, but be taken away from it back to the smaller store if they wished to purchase an item. I don’t think you would need Activity Pub for this, just a feed from the store with tags/thumbnails/descriptions/prices this could probably be handled with a plug in that linked their store to the larger site allowing their products to be searched.