Aside: I think it's funny how with an NYT subscription, you still get not only ads, but frequent article-covering ads for NYT subscriptions (asking to upgrade to a family account).
I’d assume they’re still building that profile while you use the product, but you won’t see any ads, and can still delete the data from the various points like you’ve mentioned.
I refuse to install your app just because you intentionally trash the web experience with popups.
Other people are mentioning that in the US there are two tiers of Premium, "Full" and "Lite", but I only see one tier in my country (fully ad-free, allows downloads).
But yeah, when Snapchat rolled out their subscription program, I was all set to buy it to get rid of the annoying ads and AI in my chat list, then I realized I could do none of that. So now I just use it a lot less, which is probably better for them anyway.