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?