That lets you build a dataset of these numbers correlated with all the other things Amazon knows about you. Then target you for ads.
Maybe, it notices that your coffee table is smaller than average than other similar people/apartments. They also know you have previously bought dark colored fake wood furniture before. So they advertise dark colored coffee tables to you, in the price range you would be able to afford.
Even where they are public record, there are often limits. San Francisco limits you to six requests per day, costs $0.10 per page, and must be applied in person or via mail.
I mean, I assume the tax assessors don't take a photo of you taking a shit and put it on your property record card?
I see people complaining that Amazon stuffs their face with noname amazon brand clones of anything when they search for it.
So what the EU worries about is that you won't be able to find any other vacuum cleaner except Roomba on Amazon.