It’s an interesting idea! I think there are many such applications for federation protocols.

A few thoughts/questions:

• Ideally you’ll need a stable identifier for each specific product. Most small online stores I use have product names riddled with typos, so a way to tackle that would be nice.
• What’s the data model? Would each store be an ActivityPub Actor? Like each one would have a username and publish inventory updates?
• Where do these updates go (maybe something akin to a Lemmy “community”)?
• If you’re just relying on stores’ self-reported stock levels, where’s the benefit of using a federated model? Could you just build an open source app that scrapes retailers’ websites and collates that information?
• Is the eventual goal that this competes with Amazon et al? I.e. it becomes an actual marketplace, perhaps with a “buy” and “sell” Action, and where vendors’ instances are effectively web stores?