as a result I get a list of all products that have storeview fields (like Name) personalised if they have different value provided. That's great - I can just change storeview code in the URL and it works.
The list of all would be fine if we had a list of website_ids added to product item so we could filter them out. As far as I recall it was the case with Magento 1.x API - I had list of websites that product was visible in.
I see an issue on github related to that but it died (tried to bump it, no reaction):